I haven't hunted in several years. My back is a mess (and after leaving work, choose not to get up early if I can help it).
But if I were going, and using a .44-
First I'd take the AutoMag, just to say I did it.
The Ruger 77/44 would be the most practical of the bunch.
The caliber isn't legal here, but I think it would be perfectly capable and would give me a really handy gun- that's my Ruger Blackhawk .44 Spl. I shoot it more than the others so I might do better with it anyway.