638 correction with only 2 lenses?

Would this work?
With a small Cylinder Lens sitting right on the diode?
Is this how a FAC works?

The angle of the wider axis is 35 degrees, and the narrower one is 7.5 degrees

Is there a simple calculation of the the focal length would need to be based on getting 7.5 degrees to 35 degrees?

Yes, that's how a FAC lens works. They often use a small glass rod instead of cylinder lens though. The problem is properly mounting something that tiny.

I've been able to correct one axis just fine with those cylindrical lenses, but I can't get it to work properly in conjunction with a lens like those Aixiz lenses. With other lenses I'm sure it'll work (and it does), but they're uncoated, so you lose quite a bit of power, and they also muddy up the spot.