Welcome to the wonderful world of varminting. You're goin' to "blowd 'em real good" with that round. I shoot .22-250 with 55 gr Nosler ballistic tips.
They'll violate the no fly zone...if ya get my drift!
I wouldn't worry about noise and distance. The .308 is no louder, really, than a .22-250 or other PD cartridges. You shoot, they go into their holes, they come out, you shoot.
Repeat as necessary...
One thing Art Eatman didn't mention...sometimes they don't go back in their holes!
Get some good ears...a firm table and rest, some good company and have the time of your life! ...and yes load consistency is of paramount importance!