There are at least four basic analyses of relative clauses that one encounters in the DG literature. These four analyses are illustrated with the next dependency trees/graphs of the noun phrase the people who you have called:
The analysis in (1d) is the split analysis alluded to in the question. It is the one with the longest tradition, going back at least as far as Tesnière (1959); it is also the analysis preferred in Word Grammar, and as pointed out in the question, by Eroms (2000). The analyses in (1a) or (1b) are the ones that one encounters in the Universal Dependencies (UD) or Surface- Syntactic Universal Dependencies (SUD) frameworks, and in this regard they are the ones that enjoy the greatest prominence at present.
The analysis in (1c) is the one I prefer and have argued for in my writings (e.g. Osborne 2019). I think there are solid linguistic arguments revealing that the relative pronoun should, when it is present, be viewed as the root of the relative clause; it functions like a subordinator – there are important details of my account that I am omitting from tree (1c), though; simplification makes the competing analyses more comparable.
I agree with the implication in the question, namely that (1d) contains a cycle, a “loop”, and is therefore problematic. Many DGs reject cycles and would therefore reject (1d) precisely due to the cycle it contains given that the relative pronoun appears in two distinct hierarchical positions. I also agree with the critique that the split analysis is problematic because it relies on a null element. Traditionally, DGs eschew the null elements of the sort frequently encountered in Chomskyan grammars. They argue that the existence of such null elements is non-falsifiable and hence scientifically dubious.
Concerning the example Leute, die wo sowas machen ‘people who do such a thing’. I am unfamiliar with such cases. My inclination would be to view die wo as a complex element, perhaps occupying a single node in the tree. In this regard, it might be better to analyze it as a one word diewo, or as a word and a clitic, i.e. die-wo. In any case, it would constitute a compelling argument for the split analysis only in the event that something can intervene between die and wo, which I am guessing is not possible. I also think that the DG analysis of such cases is no better or worse off then an X-bar approach. There is no harm done if one chooses to split the subordinator relative pronoun into two nodes, each being occupied by a separate element that is phonologically present. Doing so would be akin to two-part prepositions, which occur frequently, e.g. out of, in to, on to, etc.
To summarize, dependency syntax is not monolithic. There are competing analyses and one chooses the analysis that one thinks is best. This is common practice in the study of syntax in general, of course. One thing that I think many DG people would dislike, though, is being accused of producing a syntactic analysis that is “generative” in the Chomskyan sense associated with phrase structures.
The comments to my original answer are motivating this addendum. I mentioned that (1c) omits important details. I now include those details. Tree (1c) becomes (1c’):
The dashed dependency edge indicates that who is not the governor of have, and the dangling dependency edge identifies called as that governor. There is hence a long-distance dependency of a sort present, extending from called up to who. I pursue this sort of approach for all long-distance dependencies. To provide another example, here is my analysis of an instance of wh-fronting:
There is a consistency to the use of the dashed and dangling dependency edges. The dashed edge indicates that the head word is not the governor of the dependent, and the dangling edge identifies which word is that governor.
The approach to dependency syntax just illustrated with these two trees is unlike many other DGs. It is an entirely projective DG, that is, projectivity violations never actually occur. One might point out that the approach is akin to movement-based accounts. I prefer to conceive of these long-distance dependencies in terms of feature passing (think slash mechanism of GPSG), though, which means I advocate for a monostratal approach to syntax –- there are no movements or transformations, but rather just surface structures.
My DG is sometimes characterized as dependency-based GB, that is, in terms of dependencies rather than constituencies. I disagree with this characterization, though. I prefer to characterize it more as a dependency-based version of HPSG.
Finally, the critique of DG in the comments is fair and unfair, in my view. It is fair in that many DGs do ignore critical information of the sort that I include in terms of the dashed and dangling dependency edges. It is unfair in that dependency syntax is much simpler than phrase structure syntax. Dependency syntax can produce plausible analyses of sentence structures with much less effort than phrase structure syntax and in this regard, it is preferable.