I have killed plenty of deer with a 44 magnum Marlin 1894 lever gun. Never had one run out of sight or atleast sound of hearing it crash. I loaded up Hornady 240 Gr XTP over a max charge of H110. Sighted in 2" high at 50 yards put me dead on at 100 yards. Personally I like my muzzleloaders though.

The .460 is great and .357 and 44mag are good in a rifle. Henry makes a few in those 2

Unless you really WANT something different, I'd personally just stick the the ML and save the money.

The 357 Maximum or 44 Rem Mag would be a good choice but accuracy will be limited to 100 -150 yards. Probably all you'll ever need anyways. Check with Match Grade Machine "aka MGM" for a barrel for your Encore. You won't be disapointed! They should be able to make you a barrel for any caliber you need at a fair price. If you go with the Shilen select match barrel they offer you'll pay a little more. Just around $490.00 for a match grade barrel and a new caliber is well worth it, $50.00 more for a stainless barrel.