Everyone you picked out is a winner in the hunting and LR departments, with some dependent on the barrel twist and bullets selected. I've owned a .270WSM before and it had a 10t, it shot the 130/140gn great, 150's not so great. Maybe just that rifle. With a 8t, 26" barrel it could easily push the 170gn Bergers to 3100fps. It and the 280AI, could handle anything the 7mmRemMag could, within reason. Now if the 7mag is set up with a 8t and pushing 180/195, all bets are off. The 270 doesn't have that kind of artillery and the 280AI would be a little behind, but not by much.
The 6.5-284 Norma is a splendid cartridge for deer and LR. I have had one now for over 12 years and every deer I have "turned it loose on" has laid down and waited for a ride in my truck. It performs effortlessly with mild recoil and is easy to load for.
I think the 6.5-300 Bee would be great fun. Sure, it's a barrel burner if you're getting it for competition but for hunting, it's liable to last as long as the others. It would be an absolute devastating lazer with 156gn Bergers!
I shoot a .300WinMag., so the .300WSM and .300 Bee are on either side of this. Can't go wrong with either for LR hunting. 10t will do everything you're needing to do probably but I got a 28", 9t Pac-Nor just because. Either of your .30 cal choices set up this way would be a force to be reckoned with, IMHO.
Good luck, I know you're gonna have fun!