Is not possible use ordering table with per-vertex values?
I think of check compatibility between per-vertex high precision data and the ordering table: if they are in check then per-vertex is used ad it is, if they are not then ordering table is used to make a "center" position and per-vertex is used relatively to that position. From my undestanding, if possible, that would be not a perfect depth buffer, but a good enough for effects and shader in post.
Edit: This is the same idea @
Quaoar here, posted while I was whriting this stuff, and his exposition is better than mine... I hate you, Quaoar! (Just kidding

)
In my unreasonable opinion, with the preatty hacky nature of pgxp, a "per game hack" of sort is inevitable. I think about "ishiiruka" Dolphin approach: there is some options working with some games, and other options for other games, and it deals with the problem with per-game ini file.
While the psx library is huge, the games that deserve (for popularity and goodness) some heavy eye-candy is not so much: they are basically Crash, Spyro, Tekken, Residenti Evil, Final Fantasy, and a bunch of single title. With a "patreon" in mind, they are the targets for trick and wizardy.
I think that a psx emulator with jittery-free for all games and advanced effects for some games is a good enogh destination, not evil at all.
I insist 'couse your work deserve to be rewarned. The idea is around litteraly for decades, but you are the first make it works, and open source, in a scene relatively dead and/or closed source. You are the most active devoloper on this scene at the moment, or so it seams at least, and you have not even a donation link! You are like a hero.