I have same setup (the carry-handle to weaver-base screw on mount, one thumbscrew holds it, mount rides in the carry handle groove). I use Good Rings ($50+), and lap the rings (320 valve lapping compound), rotate steel bar same diameter as scope when rings are semi-tight, this makes for perfect alignment)
The rings should have 4 or 6 screws each. One for each side of the base, one for each side of the upper ring (or, two for each side of the upper ring, better..)
Tighten the handle adapter block mount down good, use 'removeable' Locktite to make sure the thumbscrew doesn't come loose.
Unscrew all of the ring setscrews to a specific distance (base of head at edge of hole, or something very repeateable for all screws). Rear Scope ring base: Screw in right side 1 turn, left side 1 turn, repeat until they are tight. Repeat for front ring base. Put ring caps on around steel bar coated w/320 valve compound that is same diameter as scope (usually 1"), same procedure, tighten one side one turn, then the other. Tighten evenly until bar it is semi snug, but moveable. The gap between the ring caps and the ring bases should be the same on all 4 parts (front, rear, left, right). Then lap the rings (10-20 strokes, spiral motion with bar), this smooths out any imperfections and makes sure the scope is mounted truely paralell, and the rings will be in solid contact with scope. Remove top rings, steel bar. Clean compound from rings. Lay scope in ring bases. Place ring tops on top of scope, tighten each side, 1 turn at a time until _tight_ (not snap off the screw tight, but tight).
I do not mean to talk so basic about this, as it sounds like you have mounted many scopes before. Hopefully somebody else will read this and be able to apply The Method. I had the same problem as you (3+" groups) until I changed rings (1.5" groups) and lapped them (sub MOA groups @100yds). Even though the scope is a bit high, but I still have the irons for backup.
Hope this helps!
-edited to remove redundancy in description, but not completely...