The short action is a non-starter with the 9.3X62. You need 3.4" or so to make it work. You could do Barsness' 9.3BS, the 350 Rem Mag necked up in that action.
To make under 7.5 pounds scoped with a lightish scope,you can get there with a #3 Douglas type contour. But you will need a light stock like a Brown Precision or McMillan Edge. You will also need to go blind mag, that steel floorplate is heavy! See mine a few posts up. Those rifles are blind mag.