North Dakota has every type of land you mention in a walking distance. We usually deer hunt in the rugged western part of the state on the foot of the Badlands. You can hunt butte to butte over long ranges in one area in the morning and be driving deer out of river bottoms and shelterbelts in the afternoon.
The long distance work is accomplished well by the Ruger M77 270Win, Leopold scope. It is the short range flushing in shelterbelts and tree line that calls for a different tool. The deer can jump up 20 feet from you. One actually came up behind me this year and ran around me to the front.
You can shoot Mule deer on the same tag in this state. OTC ammo.
Great rig and caliber for yer area as I am sure ya know.....have a considered a varible scope vs new rifle ?
a 6-24X VXIII would be tit’s for yer problem. Dial that 270 down to 6 in brush and up for range. If your in the rifer bottoms in scrub I’d say the Mini 30 would be a great rig for that. Close range , snap shooting. Lots of Winchester & marlin lever guns in 30-30 available as well in the pawn shops.
I use a 3X9 with tip off mounts and have iron sights on the rifle for close work where the limited FOV of a scope just doesn't cut it. I like to wait for my shots and harvest where the drag out is minimal, so I use 180 gr core-lokt Remington ammo, and don't track as a result, just go pick them up.
If you really want a semi-auto for the breaks, the SKS will do the job on whitetail and muleys in the draws, but I would not want to count on it for 300+ yd shots from butte to butte.
Hand pick the rifle if you go that route, try it with different ammo and use what shoots best. You might want to try more than one, but East German, Soviet, and the early Chinese ones have been the better ones I have shot. Just my $0.02. YMMV
On more thing, magazine capacity was not a problem here last time I checked with the FWS guys, you can lug around as many as you can stuff in the magazine, and a drum mag if you want to. I was settling a bet at the time, but I could just about hear his disdain for anyone who would need more than three rounds to bag his deer.
That may have changed, so I'd check with them again just to make sure you are legal. Good Huntin'!