I have a Ruger GSR in .308 Winchester. It is stainless steel and I changed to the synthetic stock to reduce weight. I replaced the sight rail with an XS system rail which allow conventional scope mounting and keeps a peep rear sight available.
The barrel is 18.7". It easily exceeds 2700 fps with 150 grain loads but could easily be loaded to reduced velocities. I would recommend this as an approach to your needs.
I owned aa 20 in barrel 99E Savage in .308 Win for about ten years. It, too would work well. So would the .300 Savage I had before that. I actually prefer the Savage performance level in a lighter rifle too.
These days, the only Savage I own is a 20 inch 1917 era TD in .250-3000. While youdidn't mention this chambering it will do a good job on most deer and has very light recoil.
