Neat result, and good writeup! I don't have time to compare them, but another resource you might look at is Daniel Lemire's "Fast Division": https://github.com/lemire/fast_division

If you've come up with something better, I'd encourage you to contact Daniel and see if he's interested in helping you write it up into a paper. He's friendly, and may be better positioned to get the optimizations into mainstream compilers.