I have two that meet your criteria. Both are on Remington 600 actions but you could use a model 7 or 700 ADL.
7mm-08 has a Douglas #1 with a 1" shank cut to 21". It is a McM EDGE Remington mountain rifle stock. Talley lightweights and a Leupold 2.5-8 scope. It weighs in under 6 pounds.
338Fed has a Douglas #2 with same shank and length above. It has a Mcswirly also in a mountain rifle contour and matching scope and mounts above. It is just under 7 pounds.
