I was load testing with my new Browning B-78 and found that with the ammo I want to use there is not enough downward adjustment in my scope. I have not tried shimming the base,and was wondering how that will work with the one piece factory base and rings I am using. Any input I can get will be appreciated.

Usually you don't have enough "UP"......Strange that you need more "Down"

If you have the B78 one piece base, you can easily shim either end. In fact, shimming a one piece base is much preferred to shimming separate bases, as the two rings remain aligned with each other no mater how much you shim.

Can you get a set of Burris Signature rings with the offset inserts to fit the base? If not, you can get a two piece weaver style base for the B78 and the Signature rings with inserts.