[scandum]

"pick a few fixed sizes and handle the rest by rounding down then a few steps of insertion sorting."

I'm late to the party, but this sounds a lot like quadsort's small array handling:

Sort 4, 8, or 16 elements using unrolled parity merges, and handle the rest with insertion sorting.

An unrolled parity merge can be viewed as a stable sorting network. I never added unstable sorting networks to crumsort due to wanting to keep the code size low, and perhaps the mistaken idea that it would reduce adaptivity, as crumsort is likely to scramble partially sorted input.