500 s&w loads overpressure?

They are definitely very long for their weight.

It's gonna be impossible to work up a 1200-1300fps load with a slow powder. Maybe with something like 2400 but it's gonna burn dirty and leave a lot of kernels.

The Lyman data I posted is for a 10" barrel. The OP's 4" barrel could help reduce those velocities substantially whilst allowing a high enough chamber pressure to successfully achieve a clean burn with something like 2400, or AA#9 (which I know less about).

My experience with 2400 has been it burns much cleaner up around 35K psi, than significantly lower. It's just a guess at this point, but I think a clean burn at 1200-1300fps it's doable. Whether or not the accuracy of such a load would be acceptable, is another matter.

The reduced case volume of an all copper bullet versus jacketed, may actually be of benefit here.