I think you should realistically count on different powders for the .303 and the 7mm Remington Magnum. As others have said, the slow burners are best in the 7mm Remington Magnum, with IMR 4831 and 7828 and H4831 and 1000 and Reloder 19, 22 and 25 being some of the most classic choices. In the .303, you want the medium speed powders. IMR 3031, 4895, 4064 and 4320 are classic choices (with my nod going to IMR 4320). Varget is also in that ballpark, as is H4895, H380, Reloder 15 and Vihtavuori N140, N150, N540 and N550.
FYI, if it were me, given the parameters you have set down, I would choose IMR 7828 and IMR 4320 and consider myself done. There are other pairs that would do an equally good (if not better) job, but those two will almost certainly give you everything you are looking for.