Personally, I would not hesitate to poke an elk with a 300 gr 44 mag at 100 yards or less, especially from a 16" closed breach Contender. I would use a flat nosed hard cast bullet with a gas check, loaded to max safe pressure and make sure I had a sharp knife in my pack. I know you said you don't reload, but there are a few ammo makers that offer such a load over the counter.
I think if you tried the 44's in the 445 barrel, you would find you're battling the same issues those who've tried the 45 Colts in the 45/410 barrels. Accuracy tends to be horrible, and mine was no different in that respect. I tried several different load combinations in my 45/410 barrel and it wouldn't hit the ground, let alone a target.
I have a 20" carbine in 45 Colt, and with Cast Performance 335 gr bullets loaded to "Ruger" levels, I'm sure no elk would shrug off one of those at 100 yards if I hit them properly.
My vote would be to pick a heavy hardcast round for your 44 barrel and "go for it". Practice a bunch first so you know you're gun and load. You could trade it for a 45-70 barrel, sure, but I don't really think you'd gain that much truthfully. Either one should do the trick.