Why would I spend $500-$600 for a rifle as ugly as the the Encore that doesn't shoot any better than an H&R/NEF?"
Maybe because you can search the NEF board and find topics related to all of these:
Chamber needs polishing because cartridges don't eject.
NEF doesn't offer the caliber that I want (anymore, or ever).
The buttstock pad screws are stripped out.
Somebody doesn't like the bluing.
The pallet-wood stock is ugly.
AND the barrels are not easily interchangeable, often requiring filing or shims.
These don't seem to be common topics on the Thompson board.
I own both TC's and NEF's. I like the NEF and have shot it a lot more, but it almost always requires tinkering to get desireable results. If you're a tinkerer, you'll love these rifles.
To answer the original posted question, you may have to search a bit, or find a 'smith who will create what you want. You can easily put a lot of work and $ into one of these rifles, but it is a labor of love. I put a Shilen 32 cal bbl into a cut stub from a 30-30 Handi and built a 32-40 Winchester, just because nobody else had one, and I wanted one. You can cut and stub just about any caliber that you can imagine within the limits of the steel.
Some here have welded a new lug onto a bbl and cut the bbl. If you have the equipment (or access to) to weld the chromoly steel properly, this would open up another window for chambering.