So, affine texture mapping is sort of a 'hardware' feature, I think there are ways to map differently in the code but then it's no longer really affine texture mapping.
I believe the way developers for PS1 games got round this problem is by subdividing the mesh to use more triangles, since this issue mostly arises when a single triangle takes up a significant percentage of the screen at an angle.
I'll look to see if there's a way to do some sort of blend between affine mapping and perspective correct mapping, as I feel that could be a useful feature if I can get it working. Thanks for reaching out!