I'm no programmer, but with the PC-FX and its games, I think there would likely be enough RAM and other resources available at nearly any given time to run a modest subtitle program. I think there's a system font available and everything. The challenge is getting it to actually work. The good thing is that I suspect that once you get such a thing to work in one game, you could probably apply much of the same code and/or techniques to other games. That's why in the long run, custom subtitle programs will likely be the best way to go.
I made a fan dub for Xanadu II, and that game has fairly few characters, fairly few lines, and is logistically very easy to work with. Nonetheless, it turned out to be a huge undertaking. Twice the characters and twice the lines per character would be monstrous, and beyond that...well, you get the point.