Seems like those things would have horrible recoil.
Recoil is real, but it's manageable. Unlike rifles, when one of these guns recoil, it doesn't slap your face or jolt your shoulder; it recoils some backwards and the muzzle flips up. With the gun pictured, a 7-08, the muzzle flips about 45 deg or so. W/ a rifle action, 14-16" barrel, scope and rings/base, these guns are heavier than revolvers or semi-autos; the additional weight tames the recoil considerably. One gets accustomed to the recoil. Muzzle blast can be a problem, especially for shooters not wearing muffs.
How far are you confident shooting a deer with that thing?
The deer in the pic was shot at 125 yds. The main factor w/ long shots is being able to get set up for the shot. On a handgun only antelope hunt I once killed a buck at 225 yds and a doe at 275 yds; both were one shot kills. I once hit a mule deer at 325 yds (unfortunately, it made a step as I shot, resulting in a gut shot; I sneaked up to it at 175 yds and put it down.) All those shots were made w/ a solid rest over a bipod, backpack, etc. Nowdays, most of my hunting is from tower stands. I rest the guns on a sand bag on the window sill or my back pack. This type of hunting is definitely challenging.