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Just bought a second hand S&B and put it on my .308 with a 0 MOA Rail.
However, the rifle now shoots very low. And the scope runs out of elevation at about 800 yds.
The mounting seems fine. Any thoughts ?

Yep - you need a 20MOA scope rail. Fairly common for anyone shooting a 308 out to extreme ranges.

Burris signature rings work very well and would be an easy way to gain extra elevation.