It's a bit of a crack theory, but I think that Early PIE had a vertical system. What's being reconstructed as *e *o are actually *ə *ä or similar, and there's a missing third vowel. This system is rather common in languages from the Caucasus, and it's likely that Early PIE interacted a fair bit with them, making it an areal feature.

I'm saying this based on:

• Almost every single time you see *ē or *ō in a PIE reconstruction, there's a missing consonant nearby; e.g. *ph₂tḗr "father" missing the nominative *-s. I don't think those vowels were already present in early PIE, so this reduces the vowel system even further into *e *o.
• Vowel raising and centralisation are way more common than vowel lowering. So why are current reconstructions proposing that Proto-Indo-Iranian, Lithuanian, Armenian, Albanian, Tocharian, Hittite, Proto-Germanic, are all lowering PIE *o into *a, instead of claiming the others do the opposite?
• Under the current reconstructions, almost all IE branches get rid of the syllabic consonants through epenthesis. They almost never do it through simple deletion, even if that's what you'd expect from typical evolution patterns. There's a missing vowel there.
• Syllabic consonants (plus *i and *u) oddly gravitate towards weird phonotactics: initial CC, medial CCC+, or final CC. That reinforces my belief that there's a missing vowel there, and syllable structure is simpler; perhaps even (C)V(C).
• A third vowel being conditionally merged into *e = *ə depending on accent would explain ablaut rather nicely.