The pronunciation of the first E in convenient follows a spelling/sound pattern that arose from a sound change that apparently occurred in Middle English.
The Oxford English Dictionary's first citation for this word is from "c1374":
G. Chaucer tr. Boethius De Consol. Philos. iii. xi. 97 Nature yeueth to euery thing þat þat is conuenient to hym.
Its etymology is given as a borrowing from Latin.
The sound change
During the Middle English period, it seems that when an "a", "e" or "o" sound was followed by a single consonant, and then an unstressed "e" or "i" sound, and then another vowel (this is a type of sequence that did not occur in native English words, but that did occur in many borrowed words), it was regular for the "a/e/o" to be lengthened. Lengthening also applied to "a/e/o" when they were followed by a single consonant and then a schwa. The word-final schwas of Middle English ended up being lost, while an "e/i" before another vowel ended up mostly loosing its syllabicity and turning into a palatal glide (/j/). So both of these sound changes can be analyzed as involving a type of "compensatory lengthening": when one syllable is lost, another is lengthened. For some reason, the high front unrounded vowel "i" was in general not subject to compensatory lengthening in either of these contexts. (In words borrowed from French or Latin, the vowel spelled "u", which had already been fronted in French to something like [y], ended up developing in English to the "long u" sound [ju] whenever it came before a single consonant followed by a vowel, regardless of what followed that vowel).
I think that the first place I saw the compensatory lengthening analysis of this sound change was in "The Architecture of the English Lexicon", by
Jonathan B. Alcántara, May 1998, section 5.2.2 "Compensatory lengthening within the stem" (p. 5-176). The sound change is mentioned in Otto Jespersen's Modern English Grammar (1954).
None of the other "ven" words that you list have this kind of "veni + a vowel" structure. "Venial" and "Slovenia" are pronounced with a long E. In fact, the preceding v is irrelevant, so you could just as well compare convenient to genius, selenium, senior, lenient, menial or to words with another consonant after the E like medium, premium, tedious, expedient.
I made a post with more details about this sound change (and the corresponding modern English spelling pattern) here: Why is “salient” pronounced with a “long a” sound?