That is a tough one. A stock pack might work but not a lot of surface area on the right side of the stock.
I've used a couple of other solutions in the past on my service rifles that are effective but not the most appealing to the eye. Foam padding held down with staples and/or tape. Works great but ugly as sin.
Another guy I know shaped a wood 1x1 to the height and contour he wanted. Lot of trial and error but worked for him. He actually drilled it in to the rifle stock to secure it. Functional but not pretty.
Assume you are raising the cheek rest to work with the rings you have? Any chance of going with lower rings or are you fitting the objective size on the scope?
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