The modern Japanese vowels /e,o/ each represent two Old Japanese vowels, arbitrarily written e ë o ö in romaji. I assume that Japanese philologists don't all use romaji, so is there a convention for distinguishing these vowels in kana?
Good question. The poster is referring to the reconstructed 8-vowel system for Old Japanese (上代特殊仮名遣) which is inferred from the presence of two ways of transcribing /e/ and two ways of transcribing /o/ with man'yōgana.
According to the Wikipedia article on 上代特殊仮名遣, there was no consistent way of indicating these in kana (naturally, since at the time the sound changes were still current, "kana" in their current form didn't exist), but that the notation 甲 or 乙, or an underline to the left or right, or katakana, or the diacritics used in transcription, may be used.
Later on in the article, 甲エ or 乙エ are used to refer to each vowel.