My second rifle ever is early '80s Winchester M70 Carbine in .270 Win. 20in barrel and slightly shorter LOP than standard (although I don't know the exact amount shorter). Very light weight, even with a good scope, and very accurate with 130gr bullets. If you can find one of the carbine models, it might be what you're looking for.
The one downside is I have never been able to find a 150gr load that it likes in the almost 40 years I've had the rifle. I think it just doesn't have enough length to get the speed needed for the 150gr to shoot well. The 180gr bullets we could get in the '80s were REALLY bad. However, 130gr are devastating.
Shot two yearling bucks from atop a cliff South of Sheffield, TX, about 500 yards from the base with that rifle at 16. Had to shoot both twice to drop them and missed out on the doe that was with them when she decided to bolt after the second yearling dropped. Would have tagged out on that lease in 10 minutes if she had stayed.
On the left is my pre-64 Mod 70 in .257 Roberts with a 22" barrel (it started life ad a 25-06). On the right is my early '80s Mod 70 Carbine in .270 Win with a 20" barrel.