Hi Jeff!
I've yet to see or fire a .375-06, but do have some shooting experience with a friend's .375-348 Winchester. That's a rimmed cartridge of course, built on a High-Wall action. It thumps pretty good with the 250 and 300 grain bullets!
Isn't here a European cartridge in the 9.3mm size that approximates the .375-06?
Just guessing of course, but I would think the .375-06 is barely more powerful than the more popular .35 Whelen.
I would guess that you'd be better off going to the .375 H&H Magnum, but in your Mauser 98, that would be a single-shot rifle because the magazine is too short for the factory round.
I'd be interested in a .375 wildcat except that the total cost of barrel, reamer, dies, and brass would make it a pretty expensive new toy. Assuming you can do most or all of the rifle building yourself, I mean. If it is done by a qualified gunsmith, it would be quite expensive.
John