The Burris rings will compensate for the scope being crooked in the rings, the shim won't, it will make it crooked, and you will risk damaging the scope tube.
1) If you put a shim in the rear, how will you properly tighten the scope ring? It won't fit properly now. 2) If you raise the rear and keep it level, now the scope tube has to bend to fit two parallel surfaces at different heights 3) If the scope tube doesn't bend, now it faces downward at the front on a flat base that will only make contact at the front. When you properly tighten the ring it will cut into the scope tube.
If might work out fine, but I wouldn't waste my time with that sort of solution, or risk damaging a scope tube.