"he is not kept from happening upon a way back."

The verb τυγχάνω can seem strange in English. It means generally to "hit" or "hit upon." It's as if something happens by chance. It often takes an accusative with a living thing and a genitive with non-living things. In this case, ἐπανόδου is the genitive object of τυχεῖν, which is completing the verb κεκώλυται (that is, the 3s perf pass ind of κωλύω).

Given the definiteness of the expression (also in Hebrew: לַ֫הַט הַחֶ֫רֶב הַמִּתְהַפֶּ֫כֶת) we are led to think that we should know what this sword is, that it was possibly a commonly known thing in the Ancient Near East. Do you think that this is possible?

"he suffers the everlasting banishment."

Here we have a contrast between someone who is "sent away" (using the verb (ἐξ)αποστέλλω) and someone who is "cast out" (using the verb ἐκβάλλω). One has the option to return, while the other doesn't. Philo is going to interpret this repetition of man being sent/cast out of the garden in connection to Hagar being sent away twice - the first time from which she returned, and the second time at which she was kept from returning. Sarah is interpreted as "sovereign virtue" (ἡ ἄρχουσα ἀρετή), given that "Sarah" is related to "minister" or "ruler" in Hebrew (שר > שרה).

Someone who is not completely controlled by evil has the option to return, but someone who has been cast out (excommunicated?) doesn't have the option of return. Adam was not given the option of return, which is illustrated by the verb used (ἐκβάλλω) and the placement of the guard (cherubim with the spinning fiery sword).

Because of how Philo interprets this section, we should imagine the words καὶ ἔταξε as missing from the verse, and the verb κατῴκισεν as governing the compound object τὰ Χερουβὶμ καὶ τὴν φλογίνην ῥομφαίαν. In other words, God ἐξέβαλε ("expelled") Adam and κατῴκισεν ("placed") the cherubim and the flaming sword. The Hebrew text agrees with Philo's understanding in making "the Cherubim" and "the spinning flaming sword" the object of the second verb (וישכן). The LXX as we have it today added a third verb (ἔταξε) to the mix.

MT: וַיַּשְׁכֵּן מִקֶּ֫דֶם לְגַן עֵ֫דֶן אֶת-הַכְּרֻבִים וְאֵת לַ֫הַט הַחֶ֫רֶב הַמִּתְהַפֶּ֫כֶת לִשְׁמֹר אֶת-דֶּ֫רֶךְ עֵץ הַחַיִּים