I've seen an article on the .350 Rem necked up to .416 and down to 8mm, but not to .375. It should be identical in performance to the .375 Whelen improved (i.e. 30-06 necked up to .375).
The .375/350 sounds like fun. It would avoid any potential head space problems. On a mauser length action it would be possible to seat out the bullets so that the base was flush with the case neck so as to provide more powder capacity in space that would otherwise be occupied by the base of the deep-seated bullet.
I read an article about a guy who did that with the .350 Rem. Mag and was able to get longer oal of cartridges by seating bullets all the way out. He was getting 2600 fps. with the 250 grain bullet in a 20" barrel.
I sold off my last 375 H&H years ago, but I still have a bunch of compoents. maybe a .375/350 Rem mag on a mil-surp mauser action would be a way to use them up.
Somebody mentioned necking the .350 Rem Mag up to 9.3 mm (.366" bullet diameter) . A very cool idea. Long throated on a mil-surp mauser length action adapted to belted cases, it should duplicate the ballistics of the old 9.2x63 mm which was basically a 30-06 necked up to .366" using 286 grain bullets at about 2,400 fps I think. The 9.3x62 mm was a classic African calliber that was considered to comparable in killing power to the .375 H&H, even thought it was slightly smaller. There are many good bullets for this caliber being made today. Nosler, Barnes, Woodleigh and Swift offer some really sexy 9.3 mm premium hunting bullets in teh 250-310 weight range. Hawk also makes a variety of weights in this caliber and you can cast your own if you've a mind to.
A 9.3mm-.350 Rem Mag? Now there's an idea! l