First, let me just say, welcome to the forum!

Karl and Franchise gave some pretty solid advice.

I've actually got an MGM custom Encore chambered in 460 S&W, and despite its recoil, I'm a huge fan of the cartridge:

Mine's 15" long excluding the brake, and according to my chronograph it gets a hair over 2,700 fps with the Hornady 200 grain FTX factory load. It's plenty accurate for those long shots, and has more than enough power to spare. It's heavy and cumbersome, so no freehanded shooting - it's strictly for those supported long shots. You could probably go as low as 10" - which incidentally will match the length of your S&W - and still get plenty of performance out of the cartridge, but I say stick with 12" or longer.

I do like the idea of a 300 Blackout or 350 Legend. Both should get you out to 200 yards or so with plenty of knockdown power to spare on deer. I would suggest the 357 Maximum since several members here have used it with good success, but since you don't handload, you're very limited by lack factory ammunition.

Other cartridges I can think of off the top of my head that would suit your needs yet still have fairly widely available factory ammo would be the 444 Marlin or the 450 Bushmaster. You could also probably make the 500 S&W work with lighter bullets.

On the subject of MatchGradeMachine, while I have a few custom barrels from them and am very happy with them, their current lead time for a custom barrel is 10-12 weeks plus shipping. If you ordered one now you may not get it until after deer season, unless you find one being sold on Gunbroker or Ebay. If you do order a custom barrel from them, keep in mind the full bull contour barrels must be drilled for the 12 gauge shotgun forends - standard rifle/pistol forends won't fit. The heavy and factory tapers will fit any rifle/pistol forend you have.