How do I map a 2D set of points to 3D-perspective correction

The front edge has a z of 1 and the back edge has a z of 2. The values were a bit arbitrary, you could pick a different value fro the back edge but then you'd need to rework the formulas. I did some fiddling with the example and stretched the perspective shapes around and actually found cases where the old method works better.

There may be a math error somewhere in my equation since it seems to need that correction for large values.

It was fine if the rects were the size they were, but those weren't their 1:1 sizes, they were both resized at the time.

At their 1:1 sizes, dividing the world width by 2.425 gives a spectacularly accurate result, so there may be a math error somewhere, but all the other numbers are so elegant that I don't mind