What bullets and powder charges seem to be shooting best for Whitetail and Antelope?

In a Remington M7MS, 20" BBL:

100gr. Sierra GK: 47.0gr. H4350: 3025fps.
117gr. SGK: 44.0gr. H4350: 2850fps.

Both group in the 1/2 MOA range in my rifle. If you Kimber won't shoot one of those two loads well, you may have a problem.

From what I've read and experienced, the various 4350 powders work the best. I use IMR. My Kimber will shoot sub MOA with 100 NBT. It will shoot 100 TSX and 120 Gameking right at MOA. My loads are:

120 GKHP 41 IMR-4350 2750-2800 fps
100 NBT 43 IMR-4350 2950-3000 fps
100 TSX 44 IMR-4350 3000-3050 fps

If I was hunting antelope, I'd use the 100 NBT. For deer, I would use the Gameking or TSX.

I'm shooting 117 SPBT Sierra's and 120 grain Hornady Hollow Points with 41.5 grains of IMR-4350 and they are going 2824 average fps.
This load is very accurate in my lightweight M96 rifle (less than .5"). This load is safe in my rifle but do work up to any loads posted.
So far I've shot 1 large Mule Deer Buck, 3 Antelope and several coyotes with the Sierra's and all gave stellar performance.
We also have a Ruger M77 ultra Light that shoots really accurate with a large charge of IMR-4064 and Sierra 100 grain SPBT's.
Good luck with yours

With 100 grain Nosler Partitions, my best accuracy is with 45.0 grains of H-4350, and Federal 210 Primers. Above, and below that powder charge, accuracy went away.