The Burris Signature rings will do exactly what you ask for, just like you asked in your first post. You can change the inserts as you need adding +/- 20 in the front as well as the back. I use them on most of my rifles and really like them. Doing this you won't have to use any rail at all - just the same bases you have - and you can adjust as needed.
The bottom of this page shows the ring height:
Scopes - rifle scopes, handgun scopes, hunting scopes by Burris Optics
Compare it to what youhave now to determine if you need a medium or high. I suspect high, but if you use a -20 in the front ring and + 10 or +20 in the back you'll appreciate it.
Using these rings I can adjust the tilt of my scope as I see fit and I'm not locked in to the angle machined into the base. Some rifles take only a total of 10, others up to 40.
If you buy the Signature rings also buy the kit with the 5/10/20 inserts as you'll need that too.