> If you want to invent scheme for understanding conjugation which works by cracking the romanized versions of words to create a pseudo-stem that could not actually exist in spoken language

That's how all conjugation schemes work. There's nothing weird about this. Stems aren't supposed to exist in the spoken language. But they are observable in the spoken language.

Compare how a modern dictionary will give you ποιέω, a full and fully-inflected word which doesn't actually exist in ancient Greek, as the first principle part of that verb. This is done because the stem of the verb is ποιε-, and the epsilon ending the stem can be easily observed by its effect on most of the conjugational endings. It doesn't happen to affect the first-person singular ending -ω (to be precise, the contraction of ε- with -ω is -ω), so the dictionary form is synthetic, chosen to be informative.