Ray,
I'm not sure how you arrived at the 20 inch figure. In a .308, it creates lots of flash and muzzleblast.
As to suggestions, I suggest you get a basic Howa, with detachable mag, in .308, with a standard weight 22 inch barrel. Then, have the barrel shortened to 21 inches and see how you like it. I think you will be very pleased.
The Howa can now be outfitted with both 5 and ten round detachable magazines.
You are correct about the Remington Model 7. The barrel is way to light for my tastes. If you fire about 3 shots within say 2 minutes, most of them open up to 2 inch groups, or larger. Just my experience.
Regards, Mannyrock