Scott,
I think if you had a good fitting custom buttstock for your carbine, a 30-30AI or 309 JDJ would be doable, with a good brake. I also think either one of those chamberings, in a 22-24" full bull barrel, shooting 165 gr partitions (or 180's in the JDJ), would be good elk medicine. I would not wish to shoot my 375 off of the standard TC buttstock. It just doesn't fit, and would hammer me pretty good. I'm still looking for a good custom carbine buttstock for mine, with a longer length of pull, and enough comb height to get a proper cheek weld with a scope. I think the factory TC stock would really whack your face big time, more so than the whack to the shoulder.
As far as the 14" or 16" pistol length goes, I have both. Most of my pistol barrels are 14" (I also have a 12" 35 Rem), and I confess I prefer that length. Most of the time when I'm shooting my 16" JDJ, I have the "range wood" on it. A large walnut grip, and the flat walnut fore end in the top picture. With it set up this way, the extra 2 inches in length really makes no difference in "feel" to me. When I set it up with the smaller TC grip set, I can tell that extra 2 inches is out there (balance wise). I don't know if that extra length is really gaining me anything (except on paper of course), as I've only had the one, and don't have a 14" version laying next to it to try and compare. I doubt there'd be much difference in recoil, or velocity, but maybe in balance. I don't care for shooting the JDJ with the TC grip set, as it doesn't fit my hand well, and makes the recoil more of an issue than a proper fitting grip does.
I think if I was going to have a 375 JDJ barrel made to order, for hunting, I'd go with the 14" barrel. Also, as much as I'm against brakes for hunting, I think this one would be the exception, and I'd order it brake'd. Only I think I'd go with a "fish gill" style brake instead of the radial brake.