Dallas,
There's a bit more to it than just moving to a fast powder for a shorter barrel. What we're dealing with here is expansion ratio. That is, the relationship of the volume of the combustion chamber to that of the combustion chamber and bore combined. This means that a 12" 5.56mm and a 12" 300 Blk will require very different powders, even though the barrel lengths are the same. With the same cartidge, you can change ER's by using different barrel lengths. By the same token, you can change expansion ratios in a given barrel length by going to a larger or smaller cartridge, such as a 20" 308 vs. a 20" 300 WM. Changing barrel lengths and chamberings throughs a complete set of variables into play and things start getting complicated. Useful stuff to understand, but it does take some getting used to.
But no, the powders ideally suited to the SBR 300 Blk, are going to be very different than those best suited to an SBR 5.56mm. I'd suggest using the same powders that are suited to a 5.56mm with a longer barrel when dropping to the 12" 5.56mm, and the same advice would go for the 300 Blk. It's just going to take a faster powder than the 5.56mm, like the 1680, N110, 296, H110, etc.. For the 5.56mm, stick with the M135, Benchmark, H322, etc.. Hope this helps a bit.