I've got a few '06 based cartridges, a 30-06, a 338-06, a 35 Whelen, 2 x 375-06 Ackley's and a 400 Whelen.
My favourite of the lot is the 375-06 Ackley.
I can use from 200 to 300 grain jacketed bullets and cast bullets in all many of weights. It will never be a 375 H&H, but it's not too far off, and is certainly more efficient per grain of powder burnt.
Mind you, the 400 Whelen is a huge surprise too, 400 grain bullets at 2150 fps with about 4-5 different powders, some of which you think wouldn't work. Basically a bolt action version of the 450/400 NE.

DC