If your crosshair is moving on the target then the gun is clearly moving - either the action in the stock or the whole works in the bags/rest. Since it's bedded I'm guessing it's a matter of moving in the bags and no amount of changing bedding or anything else on the rifle is going to fix that.
Factory tupperware stocks are horrible for trying to shoot off the bench. The forearm is generally to narrow - even for the narrowest #1 front bags, so about the only way to get a good solid front rest is to use a bipod which presents it's own problems. Then the butt stock has to much drop at the toe causing to steep of an angle for bench work which results in even the slightest movement fore or aft to cause a major elevation change down range (likely what you're experiencing).
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