I built a 6.5-06 on a pre-64 M70, I went with a Bansner stock, #1 contour 8twister McGowen barrel cut to 22". it weighs 6.5 lbs before scope and mounts, highly unlikely you will get to 7lbs with scope.
The mag box is 3.4" and if you have the barrel throated properly no problems with VLD style bullets.
It will require no mods to feed properly, brass and dies are cheap and plentiful.
I am getting 2950 fps with 140gr bullets and RL26.
Loaded round is 3.395 mag length with a 142LRAB
From left to right
140 Berger VLD