I have a reamer for 6.5x55TP, which is a mildly improved 6.5x55. It will easily do what you want with H4350, and likely faster with some slow burning ball powders. Just give it enough barrel, at least 26 inches, and it'll rip.
BTW, my silhouette rifle is a 260 rem. built on a long action. Shooting PMC 144 fmj's seated .100" into the case over a lightly compressed load of WXR powder is giving me 2925 fps with no pressure problems in 100 plus degree heat. So the larger case you want has no problems with this. Barrel life isn't all that great though.