The README mentions that it uses both (new) fixed point as well as soft floating point.

Unless I'm mistaken, the PS1 just plain doesn't support perspective correction. All texture mapping is done in hardware using a very not-programmable GPU; there'd be no way to do perspective correction, decent frame rate or not, outside of software rendering the whole thing (which would be beyond intractable).

The common workaround for this was, as suggested, tessellation - smaller polygons are going to suffer less from affine textures. Of course that does up your poly count.