“..Savage bolt action in .308 and it is (the one I bought, at least) dead on accurate out to at least 300 yards....”
My brother has one of those, and it’s the same way...very accurate out to 300 and probably even more than that if he tried.
We’re talking 800 to 1000+ yard shots though...several city blocks.
Depending on the model (I have the bull-barrelled version, pre- accu-trigger), it is a 1/2 MOA rifle; very consistent out to 550 yards. With match gade or handloads The rifle will do the job, it's really the optics that will cost you.
Average city block is something like 85 yards. I would be inclined to use something in a AR-10/15 platform just for the ability to break it down and concealability. Plenty of good rounds out there. Since they all cluster together and block the center of roads, exact precision wouldn't be as necessary as concealability so the person could get in and out. A .300 Blackout might be perfect for the subsonic round capability.