Great post. The only thing missing is a good strategy to test the resulting algorithm. Errors in arithmetic can be a nightmare.
Yet, I added several tests like dividend < divisor, close to zero remainders, a lot of random stuff just to make sure each time I add a new approach, it is correct.
FWIW, I dimly recall a numeric library, maybe a float to string, which tested everything for verification. Took a few days to run.
Then maybe use the spot checks to test for regressions. Weird compiler, toolchain, processor combos. That sort of thing.
You can definitely test against all ~2^31 IEEE 754 binary32 values to make sure that float-to-decimal conversion is correct; that's what I've done with the Rust standard library (took 2 hours per test). I believe testing all ~2^63 binary64 values are also feasible by now, but only with dedicated hardwares. For that reason I believe the library had only tested with binary32.