I'd consider looking at the Barnes data for this cartridge/bullet combo:

https://www.barnesbullets.com/wp-content/uploads/2017/10/30-06Springfield.pdf

I'd be looking at trying to drive them at 3,300 fps.

748/BL-C(2), 4064, Varget, RL-15, 760/414 would get a look from me. I don't have Big Game or I'd give it a try.

This bullet works well in the .308 Win and I've killed a couple of deer with it in my T/C Contender carbine .30-30 at a MV of 2,500 fps.