An interesting question! (with a relatively simple answer)
Within a Chomskian P&P framework, your puzzle can be explained as follows:
The adjectives excessive and farfetched are one-place predicates, assign a thematic role (presumably ‘Theme’, in traditional terminology), and, under the XP-Internal Subject Hypothesis, need arguments in their Spec A positions, which, in your examples 3a, 4a, apparently cannot but be the DPs his candour and her ideas, respectively. Hence, at the bottom of your grammatical sentences 3a and 4a, the structure is minimally [AP: [DP: his candour/her ideas] + [A': excessive/farfetched]]]. [I say ‘minimally’ because, for simplicity’s sake I will ignore here the fact that, arguably, the ‘Theme’ DPs are initially complements, not specifiers, of the adjective, which, strictly speaking, requires an AP with the structure [Spec A: ___ [A + Compl A]] and additional movement from Compl A to Spec A inside the AP, but we may leave that complication aside as it does not affect the gist of the argumentation that follows].
Concerning the nature of as, as Bowers cogently argued first in his important 1993 paper 'The Syntax of Predication' (LI 24.4, pp. 591-656), it acts as the 'functional' (= Pred) head of a Predication Phrase whose complements are APs (in this case), and whose specifier is initially empty (since Spec Pred is a non-thematic and Case-less position), although it must subsequently be filled by the ascending DPs his candour/her ideas, as they raise from their initial position inside AP to become 'subjects' of the Predication Phrase. Bottom-up, then, the second layer of structure in your 3a, 4a is, therefore, [PredP: [DP: his candour/her ideas] [Pred’: as + [AP: ‘trace/copy’ of his candour/her ideas [A’ excessive/far-fetched....]]]].
Since the Pred head as, however, has no Tense + Agreement feature complex and cannot 'check/license' either the agreement features or the nominative Case of its subject, it follows that the Case features that the DPs his candour and her ideas must contain (in virtue of the 'Case Filter') must be 'licensed' ('checked', 'assigned', etc.) by some external head (either a verb, in examples like They see/consider [me as a member of the family], or by a finite Tense head at the top of the sentence, as in your examples 3a and 4a. In the latter case, of course, those DPs must 'raise' stepwise (possibly across another argument, like the direct object me, in your examples 3a and 4a) from Spec A and Spec Pred into Spec V and eventually land in Spec T to get ('check', 'license') their nominative Case and validate their agreement features.
As to the VP layer above, although, in English, there are at least three homonymous verbs strike (same for impress), when strike/impress occur in constructions like your 3a and 4a they are similar in argument structure to intransitive ‘raising’ verbs like seem, appear (cf. Her ideas seemed to me farfetched, His candour seemed to me excessive). Of course, they differ from seem etc. in that they must select precisely as-headed PredPs, instead of the APs, DPs, PPs or infinitival clauses that seem etc. select and in that if seem takes an Experiencer it must be a PP (e.g., to me, above) instead of an object DP, but note that both ‘raising’ seem and strike, impress, etc. allow ‘dummy’ it subjects when they are followed by an associated finite CP complement (a that-clause, as in e.g. It seemed (to me) that she could have done it, It struck me that she could have done it). Non-raising verbs, on the contrary, strictly disallow ‘dummy’ it subjects, as expected.
Thus, assuming that the verbs strike, impress are, indeed, parallel in argument structure to raising verbs like seem or appear and cannot assign theta roles to their own specifiers (recall that they are compatible with ‘dummy’ it subjects), the DP subjects his candour, her ideas will gradually ascend from Spec A and Spec Pred through Spec V (V = struck, impress) into Spec T and, at the next layer upwards, the (simplified) structure of e.g. your 3a would be [His candour] [struck me [PredP: [‘trace’/’copy’ of his candour] [Pred’: as [AP (lower ‘trace’/’copy’ of his candour) [A’: excessive]]]].
Your examples 3a and 4a are well-formed and 'correct', in sum, because such derivations are coherent with all the P&P principles. Phonetically non-null DPs can only 'raise' from Spec Pred (eventually: as far as into Spec Tense) when the main verb that selects the as-headed Pred Phrase has no (future) 'subject' argument of its own, because otherwise a) the Spec V position will not be empty and available to temporarily lodge the ascending DP (here: his candour/her ideas) and 'minimality' (now, under MP: 'shortest movement') will be violated, b) if an ascending DP argument landed in Spec T, the verb's own DP argument sitting in Spec V (a thematic, but Case-less position) would not be allowed to also ascend into Spec T, its Case feature would not be licensed, and the Case Filter would be violated, and c) if the main verb assigned a theta role to a DP argument of its own in its Spec V and the 'ascending' DPs (his candour, her ideas, in your examples) somehow landed in that non-empty position, they would end up discharging two theta roles (one assigned by the adjectives excessive/farfetched, the other assigned by the main verbs strike/impress) and the Theta Criterion would also be violated. [Of course, they cannot possibly land in Spec V if that position is occupied by the verb’s higher argument and eventual subject]
Suppose now that, accepting that derivation, we tried to ‘passivize’ 3a. The result would be your 3b, with the (simplified) structure [I] was struck [PP: by + his candour] [PredP: (‘trace’/’copy’ of his candour) [Pred’: as [AP: (lower ‘trace’/’copy’ of his candour) [A’: excessive]]]], but, unfortunately, such a structure/construction violates a key principle of P&P grammar: 'traces' (/'copies') must be 'c-commanded' (and ‘bound’) by their antecedents. Note, however, that, if his candour is turned into the complement of the preposition by, it will no longer c-command* any of its traces. Recall the standard definition of ‘c-command’: A c-commands B if the first branching node C dominating A also dominates B; now, in the PPs by + his candour/her ideas, the only node that the DPs c-command is the P head by, because the first branching node above them is a P’ and, of course, P’ does not dominate the following PredP nor the traces left behind inside it by the ascending DPs]. As a consequence, the resulting passive sentence 3b is correctly predicted to be ungrammatical. The same applies to 4b, of course, if we try to make 4a passive.
But, is there no other derivation of 3b, 4b that can satisfy the principles of P&P and allow them to be grammatical? For example, what if we assume that strike/impress are parallel in argument structure, not to 'raising' verbs like seem, but to non-raising transitive psych verbs like frighten that do assign a Stimulus theta role to their subject and an Experiencer role to their object, as seems to happen in 1a or 2a? Under such an analysis, of course, His candour/Her ideas must be directly generated in Spec VP and raise into Spec T to check Case, etc., as they do in 1a and 2a. Correspondingly, if the construction is (made) passive, we must expect them to appear after the preposition by, as in 1b, 2b. As all four are grammatical, such examples raise no further issues.
The cases containing as Pred-Ps, like your 3a-b and 4a-b, however, are a completely different story: since the as Pred Phrases contain the one-place adjectival predicates excessive and farfetched and these, as stated above, assign a thematic role that must be satisfied by an AP-internal argument, P&P theory would predict them to be ungrammatical unless we claim that that indispensable argument is satisfied by a phonetically null category, but which? Of course, it cannot be a trace of His candour or Her ideas, for reasons already explained in paragraph 8 above, so the only alternative is a PRO controlled by the DP subjects.
Thus, under these alternative assumptions, the simplified structure of e.g. 3a would be [His candour] [struck me [PredP: PRO [Pred’: as [AP: trace/copy of PRO [excessive]]]]], which satisfies Theta Theory and solves the interpretation problem. Case-wise, such an analysis raises no problem, either: PRO can only receive Null Case (or, being phonetically empty, no Case at all, depending on which theory of PRO is adopted within P&P meta-theory), but, either way, it is fine in both Spec AP and Spec PredP. Movement-wise, PRO need not (and, in fact, by virtue of Economy, cannot), raise beyond Spec Pred (i.e., there must be PRO-raising from Spec A into Spec Pred, but there cannot be any subsequent PRO-raising from PredP into any higher specifier). Thus, in sum, claiming that the apparently missing argument of excessive or farfetched is a silent PRO solves the interpretation problem and causes no Case, Theta Criterion or Movement Theory violations, which accounts for the grammaticality of the ‘active’ sentences 3a and 4a.
The only crucial condition that PRO must satisfy is that it must be ‘controlled’ (and therefore c-commanded) by the subject DPs (his candour, her ideas, in this case), and that is where the fatal difference arises that makes the passive versions 3b and 4b ungrammatical: as soon as his candour/her ideas are construed as the complements of the preposition by (cf. I was struck/impressed [by + his candour/her ideas] as excessive/farfetched) they will no longer c-command the PRO subject of the following PredP, PRO will no longer be 'controlled' (= able to co-refer with its intended antecedent his candour/her ideas), it will therefore have to be interpreted as 'arbitrary in reference', and the resulting passive construction will become uninterpretable and ungrammatical.
In sum: no matter which of the preceding analyses of the argument-structure of the verbs strike and impress is adopted, P&P Theory straightforwardly predicts that passivization will not be possible in such constructions as your 3b and 4b. The reason is essentially the same in both cases: once the subject (or derived subject, if strike, impress, etc. are raising verbs) is construed as the complement of the preposition by, it can no longer c-command either its trace(s) – under the first analysis - or the associated PRO(s) – under the second one, the respective derivations violate Trace/Control Theory, and the resulting sentences are ill-formed. (In current ‘minimalist’ terms: they ‘crash’ at the C-I interface).
As promised above, then, your interesting question has a straightforward answer: granted P&P theory (or its subsequent minimalist versions), no stipulation is needed to explain why your 3b and 4b are impossible in English; their ill-formedness follows directly from general principles of the theory, as should always happen in science, including scientific linguistics.