Interestingly, doing a similar analysis where we bucketed each word into 243 (3^5) buckets based on the possible result, we found "RAISE" as the best word. Source[0]
I would say that the distribution of yellow letters in the remaining word determines the value. If you have a yellow "X" or "Q" or one yellow vowel after testing all 5 vowels, that is a lot more meaningful than a yellow "T", which could really go anywhere. A yellow "G" but grey "I" tells me (at least intuitively, not quantitatively) a bit more than a green "I" and grey "G".
A recent word had a single vowel. This made it reasonably easy to guess where those vowels could go and to also choose a consonant-heavy next word that would really tear apart the search space if even one consonant was valid.
I think I'll switch to using RAISE or SLATE as a first choice. It was ADIEU before, but there's almost never an A in slot 1, U in slot 5, or D in slot 2, and I don't feel like any of these letters has a significantly most common position with just the info from these 5 letters. The yellow/grey letters are helpful after ADIEU, but I still need to explore at least 4 more letters (including O, and usually N or C) to even get a good idea of where any matches might go. In the moments that letter 4 is "E" while guessing ADIEU on round 1, that actually doesn't help me much with round 2. In fact, then I'm faced with the decision to explore unguessed letters in general, words with two "E"s, and/or words with "E" in 4th position. (same with "I" in 3rd)
I've implemented your last suggestion of scoring words by how much they reduce the pool of potential candidates (12k+). Testing it against the 1,000 most frequent words (targets), the word LORES seems to work best on average.
[0] https://gist.github.com/popey456963/a654e98d0180566b897b70ee...