Rammer: How tall are the rings? How is your cheek weld?

I have a Colt Delta H-Bar. It came from the factory with a scope mounted on top of the carrying handle. The rifle is clumbsy. And there is way too much distance between bore and center of scope. I want to put together a Varmint rig out to 300 yards with a black rifle(While we still can). My major concern is scope mounting.

I am looking at the Rock River. I am trying to decide between the Predator, and the Varminter with the raised bases. Tom.