I stayed up late last night, elephant fever knows no time line, playing with ballistic and recoil tables comparing the 375h&h, 375wby, 416rem and 416rigby (Which I've sort of ruled out. With the high cost of brass and the fact that it takes more powder to equal the same velocity of the Remington.)
Here the numbers:
375 h&h\300gr barnes soild\2500fps mv\3300ft.lbs. energy @ 100yds\33ft.lbs. recoil.
375wby\300gr barnes soild\2600fps mv\3585ft.lbs. energy @ 100yds\37ft.lbs. recoil.
416rem\350gr barnes soild\2500fps mv\3995ft.lbs. energy @ 100yds\44ft.lbs. recoil.
416rem\400gr barnes soild\2350fps mv\4065ft.lbs. energy @ 100yds\47ft.lbs. recoil.

So why not the weatherby? Based on these numbers for 4 more pounds of recoil you get 385 more ft.lbs of energy.

What weight are you figuring for your rifle? To send a 300g at 2600 fps with about 87g of powder you need a 12# gun to make only 37 ft lb, if my math is right.
Well, it looks like you still have time to get Bridger to make a 350g solid, which would do about 2400 fps ~45k psi from the 375 Whetherby.
So add to the list:
375 Wby\350g BS\2400fps\3670ft lb @ 100yds\40ft lb recoil.
That's smack in the middle of your list there, for the buffalo and for you.
And the SD on that sucker is about .355!