"More powerful" and "flatter shooting" are not necessarily the same. The 35 Whelen is more powerful than the 30-06 and shoots about the same trajectory, but not flatter. If you want flatter shooting, but don't want a lot more recoil and muzzle blast, then try the 300 RCM. It will give you about 75 fps more velocity, with very little more recoil.
The problem with velocity is, it takes a lot more powder to make a little improvement. So if you really want flatter shooting, you need a pretty big boost in case size, which means a lot more recoil, blast and expense. To gain 4" in trajectory at 400 yards with a 180 grain .308 bullet, you have to double the recoil. Is it really worth it???
Mono-metal bullets like the Barnes TTSX give tremendous pentetration and tissue destruction with much lighter than standard bullets. You can gain 2.5" of trajectory with the 150 grain TTSX in the standard 30-06, and actually have a little LESS recoil than the 180 grain load. If you handload, I'd go that route.