At those ranges you'll be happy with irons unless you problems getting a good sight picture. A scout mounted red dot optic would probably be your best bet for fast target acquisition.
I used to use a BLR in .358 Win to hunt hogs while walking in the brush and checking the hog traps. I now use a Rem 141 in .35 Rem for my 'brush' gun. Either one of those rounds will flip a hog on its ass and so will a .308 Win. Yes you can mount a scope on a BLR something with low magnification like a 2.5 would be best in a straight power scope or a variable like a 2-7 would be nice as well.
This older Savage 99 lever action in .308 has downed a lot of game for me. It shoots 180 grain Remington or FEDERAL equally well. This big buck was toppled with one shot. I fired cross canyon from the tree line in background.
This scope is a TASCO 4X compact from the early 1980's. It is far superior to the Weaver K-3 that I had for many years. TASCO made 'em in Japan during that time. Current TASCO scopes are made in China and I have no experience with them. Simmons and Bushnell still build quality for affordable pricing.