FWIW: here in Ohio we're allowed a 5" barrel.....
but here's what i think otherwise: if a .44 mag' is your recoil limit, but doesn't shoot flat enough then think about a .41 mag' which some say shoots flatter. it will still kill deer, hogs, black bear, and so on.
i'd go with a .44 mag myself, with a bullet of approx' 210 to 240 gr's to achieve high velocity with sufficient energy downrange. i'd do that with a Jacketed HollowPoint, too......which i've noted elsewhere as recommended by dick metcalf --- and j.d. jones who sold molds for lead bullets! i've used hardcast lead for my .44 mag'; but i'm not pushing it to its velocity limit with the longer barrel of a T/C which might give you a problem with leading unless using a gas-check'd design.
i'd get the longest barrel i could get on that T/C to make good use of what velocity can do to stretch your trajectory and killing power. i have seen whitetails here in ohio that go well over 300 lbs........... you can find them in a number of our counties if you're willing to wait for a big one to come along. with a scope you can take a big deer at 150 yds' with the right bullet if you know your trajectory and have practiced.
if you get a .357 Maxi' you may get the flattest trajectory yet, but you'll top out with 200 gr' bullets which have a relatively small diameter. at least the .44 mag' starts out with a better diameter, and can go with enough weight to Easily penetrate a deer through both shoulders if need be. we get enough hunters out on public land in this state that it can make a difference on who tags a deer if it isn't put down Quickly.
good luck, Handi'
ss'