Shiming mounts is not a good idea it can be done but it tends to bend things .
A much better solution is a tapered base.
I presume the Rock River mount is on Weaver or Picatinny rail.
If it is a removeable rail , then it can be replaced with a tapered rail say 15 or 20 MOA taper .
If the rail is intergral and I think it may be on an ATH and can't be removed then the next best option is a new mount with the taper built into the mount like ARMS
MSP Variable Eye Relief Scope Mount and 30mm Rings with MOA: MSP Scope Mounts
This mount has 3 heights of rings and lots of ring spacing and eye relief options plus choice of 15 , 20 , 25 and 30 MOA taper .
Also you can buy a set of ring inserts for mounting 1 inch scope tubes in the 30 mm rings .
Works best on a rail that is right on specs. However if it's to tight and will not lock up teh locking claw can be gently hand lapped witha stone until it locks tightly . If it's too loose you have a problem and the loose protection plate between the claw and the rail taper will need the outside surface to be built up with a steel shim glued inplace with epoxy .
This is generally not a problem with commercial made rails.
I would contact Rock River and ask them if the rail will take an ARMS QD mount , it should.
Another option is aska local gunshop to get you one on the proviso that it fits the rail nicely . Tight by hand .
This would also be another option and would fit out of spec rails http://www.mountsplus.com/mm5/mercha...de=127-NKO-743