FYI - That .30-06 RSI weighs 6lbs 4oz, bareback, on a baby scale.
It used to wear a 7.5oz 2.5X scope (that had 5.5" eye relief) in Ruger rings, coming in at an ounce over your critical mass of 7 lbs - but I decided to switch to a "no-batteries" IR scope, and mounted the 11oz Trijicon Safari - for a grand total of 7.5lbs, less sling, etc.
The best way to reduce a #1's weight further is to use a NECG peep ILO any scope - which is the way I went on one of my .45-70 #1-S'.
You msut have gotten one with a not-very-dense stock, since they catalog at 7, and of course they ususally lie on the light side.
I always thought that little peep was the perfect sight for the lightweight straight stock .45-70.
