The only answer for this I can come up with is that this is some kind of "inversion" like that which occurs in languages like German and Dutch. If so, there must be a "trigger" that causes the verb to push to the beginning before the subject and object as it does in two relative clauses of the Laris Pulena inscription (TLE 131). I've parsed the relevant sentence with some helpful modern punctuation as follows:
Χi-m, culsl leprnal,The two instances of pśl, I believe, are referring back to the genitive phrase culsl leparnal. In each of these relative clauses, we find the verb at the beginning, ahead of any unmarked nomino-accusative nouns. In the first clause, the preterite verb cerine precedes what may be two nouns, pul and alumnaθ. (I've abandoned the idea that pul is a relative pronoun declined in the type-II genitive, which should probably have been written *pl if it were so, because it causes too many structural and semantic difficulties in this passage.)
pśl varχ-ti cerine pul alumnaθ, pul hermu huzrna-tre;
pśl tenine eprθnev-c meθlum-t pul hermu.
In the Cippus Perusinus, the phrase ipa ama hen 'that which is forth' might also suggest this same sort of "verb-forwarding". Afterall, if we understand hen to be an adverb, we might expect *ipa hen ama in a more well-behaved SOV language. Again, we see verb-forwarding in the presence of the relative pronoun.
However, if the relative pronoun triggers word-order inversion, it doesn't appear to be a consistent rule since in TLE 27 we read:
[...] in-pein mler usi ateri.Here, the verb ateri follows the object mler in a clause introduced by in-pein 'where, at which'.
 Odlin, Language transfer: Cross-linguistic influence in language learning (1989), p.94 (see link): "Studies of Dutch and German offer particularly intriguing examples of where word-order transfer can lead to different acquisition patterns. Both languages employ SOV in subordinate clauses and SVO in main clauses, although other main-clause word orders are possible under special circumstances."
 Bomhard/Kerns, The Nostratic macrofamily: A study in distant linguistic relationship (1994), p.161 (see link): "Thus, in a consistent SOV language, an attributive adjective or a genitive precedes its 'head' noun, an adverb precedes its adjective or verb, a noun precedes its case ending or postposition, [...]"