I always a little more than suprised at the number of people (at one time, myself included) that wonder why .375 bullets do no work in a 38-55. It's like using 45 Colt bullets in a 45-70, same caliber, right? Wrong.
The 375 Winchester caliber was designed for .375 dia bullets, but the 38-55 never was. They were always in the .378-379 range, so it's no suprise they keyhole. Not trying to put anyone down, so please do not take it that way, but I too have learned the hard way, after plunking down hard earned cash, something we could have easily read beforehand.
For ONCE I did my homework first, and when I bought my 38-55, I did so knowing it most likely would never see a jacketed bullet. I MIGHT see smokeless powder, but not sure yet.
I'd suggest giving up on jacketed bullets, and getting some good cast bullets for it. You push them about as hard as you need to in this caliber, with a GC 250gr bullet at nearly 2000fps, it will stop most any critter in the country.
Please let us know how the chamber job does for ya. I must have beem one of the lucky ones since I can slide .380 dia bullets into mine with no issues.
By the way, the Handy and the 38-55 brass will handle any load you can find in any manual for it. I use 38-55 brass in my Winchester 94 BB with some warm 375 Win loads and have yet to see any brass issues from it.