No expert here as I've been to the DC twice but only once to hunt and that was for PG only. Were it me I would take the '06 (if that's what you decide on) along as a back-up but plan on the 375 for everthing. While I used the H&H iteration--and it worked perfectly--I now have the same rfle you have. I did have the stock re-enforced with an addition cross bolt added and the action glass-bedded with particular attention to the tang area. I also have a McM McWoody coming for it.
Again, I used the 270-gr TSX at a sedate 2675 fps and still only one was stopped and that was by a very hefty Burchel's mare zebra after breaking both shoulders and ending up under the off-side hide. That's if you don't count the one that hit a little-finger-sized twig thirty feet in front of a nice water buck. It stayed on course traversing the buck's chest side ways and stopped again under the hide.
My inclination after using it would be to just go with that 270-gr TSX over a good load and make it your go-to. If you are starting out with the 375, take your buff, then carry the '06, you might meet buff again which is why I would just go 375. You could use Horn 270-gr Interlocks for practice. If your experience is anything like mine, you certainly will not feel overgunned on PG; I can't speak to feeling under gunned on buff
I found practice over the sticks here to have paid very good dividends in ability and confidence once over there. You have to figure out the most comfortable placement of hands and rifle on the sticks and that only comes with doing it.
My .02 cents worth.
