I see a couple of issues here.
The Model 70 Featherweight came out 68 years ago. It was considered light then because people were comparing it to Model 70 Standard Rifles and Remington 721s that weighed 10-11 pounds or more with a scope. Today the Model 70 FWT is one of the best general-purpose hunting rifles anywhere, but it hasn’t been the place to start for a mountain rifle for about 20 years. That said, you should have no problem bringing this one in right around eight pounds.
The M-70 has tons of mounting options, but scope tubes have gotten shorter over the last 15 years and that’s the real source of your problem. I don’t like the greater height of a rail, so I like Weaver-type bases (
https://www.midwayusa.com/product/1477716946). I install them so the cross-slots are close to each other—in the pic at that link, you’d rotate the one on the right 180 degrees. Something like these bases (
https://www.midwayusa.com/product/100886220) will give you even more options. I also like Weaver low or extra low rings because they're cheap, bomb-proof, and they return to zero. Here’s a shot of them on a short-action Model 70 from another forum. If this were my rifle, I'd reverse the position of the bases to get a little more mounting room and more latitude to get eye relief just right.
Burris Zee Rings are narrower, which gives you more flexibility in mounting position as seen on this long-action Model 70 FWT with Warne Weaver-Style Bases, Low Burris Zee rings, and 2-7x33 Leupold:
On any long-action Model 70 with a modern scope, you're going to have trouble getting eye relief just right, but that's part of the joy of owning a long-action Model 70.
As for carrying your rifle with your thumb between the scope and the bolt, try it with the floorplate against your palm, slipping your fingertips between the scope and the top of the bolt instead of your thumb.
Okie John