Unless the scope is 12" inches above the receiver, there is no way an elevated base, 20 degree base, or mismatched rings could cause a 100 yard zero to shoot 6" inches high at 200.
The trajectory of the .338 is fairly flat, but it's certainly not still climbing at 200 yards if it is truly zeroed at 100 yards.
As you stated in your OP, if it is zeroed at 100 yards, it should be dropping about 3" at 200 with a normal 2.5" scope height above the bore.
Any of the above mount problems would simply not cause it to shoot higher at 200 then it is at 100.
The Laws of physics prevent that from happening!
rc