"man of many turnings", is a more literal translation of polytropon than Lattimore and Fagles, and and in fact the whole line is better analysed as an original, literal translation from common dictionary glosses than a "crappy mishmash". Many people who want to give a literal gloss say "man of many turns" or "many-turned man".

> ἄνδρα μοι ἔννεπε, μοῦσα, πολύτροπον, ὃς μάλα πολλὰ πλάγχθη, ἐπεὶ Τροίης ἱερὸν πτολίεθρον ἔπερσεν·

man(acc.) me(dat.) tell(pres. imp.), Muse(voc.), many-turn(acc.), who(nom.) very(adv.) far(acc.) wandered(aor. 3sg. m.p., but note active sense of "to drive off"), after(adv.) Troy(acc.) holy(acc.) city(acc.) (he) sack(aor. 3sg.)

Glosses my own, text from https://scaife.perseus.org/reader/urn:cts:greekLit:tlg0012.t...

Claude repeats man twice like Fagles, despite that not being in the Greek. Using driven and wandering is a weird repetition rather than just using "made to wander" which is a more natural way of directly translating the passive. Claude uses the "driven" in both Fagles and Lattimore. It also drops the "very" for no apparent reason (also not present in Fagles or Lattimore). Claude uses "once he had sacked Troy's holy citadel" mirroring Fagles's phasing, when you could just translate it "after he sacked the holy city of Troy". It also uses citadel rather than city, copying Lattimore.

Vis-à-vis polytropos, I just think that "man of many-turnings" sounds god-awful, but the similarity was mostly the fact it uses the construction "man of x" like Fagles and Lattimore rather than a normal adjective like in the Greek.