Since you are a handloader, I would say ANY .30+ caliber should work and work well. I have a 10" .357 Mag that I love shooting. It is very accurate and I trust it to take any deer or hog in my parts out to about 125yds or so. I also have a .30 Herrett 10", and it shoots just as well, but recoils more with full power loads, but is also flat enough to shoot out to at least 125 with my 4x scope, and I have shot it to 200, and it grouped well enough that I think I could make that a realistic range for me assuming I have a rest available when the moment comes. Recoil is manageable, and I think less than my .44s, but it is more than a .357 mag. My .44 mags are a 7.5" Ruger Vaquero, and a 14" Contender. Using factory ammo, neither is comfortable, but the Contender hurts a bit. Now this is one thing I dont understand, but shooting handloads out of these same guns, in loads that exceed the performance of the factory stuff (checked with a chronograph) isn't bad. The Vaquero is still slightly more comfortable, but I have always been more comfortable with a single-action type grip frame than a double-action, and the Contender is very close to a double-action frame/grip design. I have settled on a load that is slightly lighter than factory .44 mag, but due to the lack of a any venting like a revolver provides, it equals performance of the .44 mag in a revolver, and shooting those in my Contender is actually comfortable, and still flat enough out to 115yds for deer with a dead-on hold, so I use that, and it works well with my 14". I have been seriously considering making a 10" .44 a priority soon though because I just prefer the balance of my 10" barrels over the 14". Haven't made up my mind yet though, because that 14" shoots very well.
I just think that being a handloader, you can take a caliber that may recoil on the limit of your comfort level, and load it down somewhat and end up with something that should be much more comfortable, yet give you the option of going to full power as your comfort level grows. I can't speak on the 7 TCU, or .223 for deer, but the .30 Herret I have loaded from very light subsonic small game loads on up to the limits (per the manuals at least), and it is very versatile, but I haven't seen any factory ammo for it yet and dont expect to, but that shouldn't matter since you load like I do. .357 is great, as is .44, but another option which has been mentioned is a .45 Colt. Mine are all revolvers, but it would seem to be great in the Contender since it is a strong action like my Rugers so you can load it as light as you want or as warm as safety and common sense allow.