Jason, the short answer is yes, the Handi will easily handle 375 pressures. The 375 Win operates at 52,000 psi with a case body diameter at the head that is smaller than the 30-06 which operates at the same practical pressures. I've fired quite a bit of 375 Win level loads in mine, no trouble. There is a slight mismatch of chamber dimensions to bore dimensions, and the bore is sized to the older 38-55 size of 379-380 on the groove diameter while the 375 Win is a true 375-376 on the groove diameter.
While a few are experiimenting with jacketed bullets in the Handi, I believe you can do as well with lead. The twist handles the Lyman 264 grainer (379449) quite well and pushes it at 1800 fps comfortably. I believe more is attainable, just don't have a chrono at present to be able to figure it out.
The main problem with the Handi and the 375 is not pressure but bore size. A couple of folks are making a 379 jacketed bullet, but makers like Speer, Hornady, Sierra are making a 375 bullet and it tends ot tumble in the .004" larger Handi barrel.
Do a search, cheatermk2 has done a bit of experimenting on this line with the Winchester bullet (no longer a component production item) there has been a good bit of disscussion on this subject over the last several months.
I don't think you can go wrong with even a 250-270 grain lead bullet at 1700-1800 fps. Such loads have worked for close range work on deer and black bear and hogs for longer than we've been walking around, at it's worst the 38-55 is the ballistic twin of a 44 Mag rifle, with a better bullet.
