Which US battleships receive modernization priority

If the 1920 South Dakotas were built, would they and the Colorados be modernized first?

Yes; the Navy would prioritize its more useful 16-inch-gun ships.

If the 1920 South Dakotas and Colorados both existed, their 16-inch guns would put them first in line for modernization. That priority would follow their usefulness within the proposed fleet. Older standards would fall behind these heavy-gun ships when refit choices were made. No detailed modernization package is prescribed beyond that ordering.