Okay, I'm on a device where I can actually type out long responses.

Isn't the answer obvious? Get an Encore chambered in 460 S&W! That's the best compromise. Okay, I'm just kidding. Although that is something I'd like to do at some point come to think of it.

So, the Model 460. . . . It's a powerful revolver. A handcannon. An absolute beast of a handgun. Between the recoil and muzzle blast, it's quite a lot to handle when you touch a round off. I never quite got to the point I could comfortably handle the XVR. That said, you've clearly got some experience with shooting hunting handguns. My best advice to you would be to see if you can find someone with a 460 and ask if you can try it out. That way you could get an idea of what to expect, and whether you think it's something you'd like to pursue. I'm aware that's probably a bit of a stretch.

On the subject of the Encore. There's a lot of options that are more comfortable to shoot than the 460. Hell, my 300 Win Mag kicks less, although with its brake it's just as loud. The only caliber you've mentioned that I've tried is a 243 Winchester barrel, a T/C factory 15" barrel to be specific. I rather liked it, but I ended up getting the 300 barrel because I felt the 243 in an Encore pistol would be marginal for deer. Just a personal opinion, you may feel differently. There's one thing I noticed, though, that you might need to consider. While it's true I wasn't pushing the maximum loads listed in the manual, a potential deer hunting load I came up with drove a 95 grain SST at 2,500 fps. I could have probably pushed them about 100 fps faster, but I digress. The important thing is the 95 grain bullets weren't very accurate at all, and after running the numbers, I don't think they were stable at those speeds with the twist rate. The factory barrels are 1-10", and if you want to use the heavier deer hunting bullets, I think you need a bit faster twist to be able to stabilize those heavier bullets at those speeds. I talked to another guy who had a 1-10" twist Scout pistol who had the same problem. He said he found an 80 grain bullet that worked well, though.

In addition to the 243, looking at Thompson Center's website, you can buy a factory 15" barrel in, 7mm-08, 308, 30-06. Needless to say, all three of those are great options to choose from. The 7mm-08 is probably the one I'd recommend, if I had to choose between the three.

One last thing on the subject of Encore barrels: if you decide to go that route, I highly, highly recommend getting MatchGradeMachine to make you one. Their basic barrels are similar in price to T/C factory barrels, but they are very good quality and highly customizable with regards to length, contour, crown, twist rate, and especially the absolutely ridiculous number of caliber options they offer. Want a 6mm Creedmoor handgun? 350 Rem Mag? 458 Lott? You can made an Encore pistol barrel in it.

Hope this helps.

I take it you’ve found a used 243 Encore pistol for a good price? Nice.

I guess the 338 Federal would be pretty good, but I think you should go with a 338 Win Mag instead. No brake.

Oh, one more thing I thought of. If you go with a bottleneck cartridge and decide to reload, I’ve found the faster burning powders listed for the cartridge tend to work a bit better in those short barrels.

Keep headed down that road. You’ll come back to your senses sooner or later.

The powder which gives the best velocity in a rifle length barrel will do the same in the short barrels.

While I trust your judgment, my 300 and (former) 243 barrel seemed to prefer otherwise. IMR 4064 worked well in both.