You already have a .44 Magnum. Hunt deer and bears with that, not with a CC .38 or .357. If you want your CC .357 to be a good trail gun, get the 3" SP101. You could certainly shoot a deer with it, and it would certainly kill it within reasonable range. I have killed a deer with a small little pocket 9mm, after all, but it wasn't hunting. It was a head shot to put down a crippled deer at about 10-15'.
But when you go out deliberately to hunt, carry a hunting revolver. It's much easier to make a clean kill that way.
I don't like the Judge. I have friends that have them and love them. I just can't get around all that cylinder length if I'm going to have it loaded with .45 Colt - what a waste of steel. And I can't really consider .410 to be a very good defense load, as I've seen it's non-performance as a rabbit hunting shotgun.
I usually pocket carry a S&W 642 for personal defense in the small town I live in. In the mountains, where we have small black bears and lions, I belt carry a S&W 13-3, 3", loaded with heavy, wide-flat nosed .357 loads going over 1100fps. I use the same gun as my hunting backup revolver - which is for putting down crippled game at close range without blowing up a head. When I go to the city, I usually carry a full-sized 9mm with a big magazine and a spare on the belt, if the weather allows it, or if it's really hot, just run that same 642.
Use the right tool for the job. You've got framing hammers, ball peen hammers, sledge hammers, big screwdrivers, little screwdrivers, files, chisels, knives, saws of various descriptions, wrenches and sockets and so forth because each does the job it's designed for better than any other tool can be made to try to do that job.
In the same way, no one gun is going to be able to do all the jobs that you seem to require. You want a CC personal defense pistol. You want a trail pistol for close-in defense against black bears. You want a deer hunting pistol.
I see that as needing at least two, and preferably three: a pocket revolver, a light belt gun, and a heavier belt gun. You could get away with having two - the pocket revolver and whichever belt gun you decide to go with.
Which .44 Magnum do you have? Your trail gun issues may be already fixed, just with that. Certainly, unless it's a weird snubby .44, your hunting needs should be.