This is one of those situations that you need to go and and handle alot of different guns and see which ones come up to the shoulder best for you...Myself, I don't care for the Remington semi rifles, just don't balance well and are heavy...Which brings up another point, how much will you carry the gun??? The Ruger in 44 Mag I would expect to be fairly light, but I don't know how well it balances...A good lever action 30-30 or 35 Rem is a hard gun to beat if you carry alot...Even though you can't use buckshot, have you considered a slug shotgun, there stocks are made for wing shooting, I have a Remington 1100 that will group foster slugs into a 1 1/2 inch group at 50 yards, and its devastating on deer....
Another thought...My brother has a Remington Model 7 in 7mm-08...Its a light weight quick handling gun...I personally don't like such a short gun because I'm 6ft 5...It just feels too short....But I can tell you, I have shot running deer with my bolt action .243 with a Leupold 3x9x40...I can cycle the bolt plenty fast by not taking the gun from my shoulder...Here in NC, where the neighbors run dogs, I have used this gun to down several running deer....They run through my property and its the only way to teach those good old boys a lesson....Now, I'm shooting from a tower or a tree stand, so all shots are down to the ground so its pretty safe....Point being, if the gun fits you properly and the scope is set up properly then you can be fast enough with a bolt gun and a scope and a short action like the 7mm-08 or the .308 will do the job...