The rifle may be off as the bore sighter seems to tell you, but the bore sighter could just as easily be the problem. I've got one that's way off and another that is much closer. Neither is perfect.
Look through the advice you have and follow suggestions one at a time. Without spending money (I'll never pay for weaver rings again) you can try a few things. This usually gets approval pretty quickly with the honey.
Check that both bases are stamped with the correct number, and remove the bolt from the action when tightening them down. *one thing not mentioned is that occasionally the screws shipped with a scope mount are too long and actually go right through the receiver and hit the bolt, which makes you think everything is tightened down when it's not.
Center the reticle in the scope before mounting it.
Mount it as instructions say, then boresight it.
Next put it in a solid rest and align the crosshairs on a distant target. Being extremely careful not to move anything, lower your head and look through the bore, centering as well as you can. The "target" you've aligned with should appear reasonably centered in the bore. If the target is not visible in this step, the problem is likely the bore sighter.
If you make it this far without problems, remove the rings from the base, still attached to the scope, and swap the front and rear bases on the receiver. Remember, no bolt in the action through all of this.
Reattach the scope to the rail, and alignt the crosshair with the same target while on the same sturdy rest. If things have changed dramatically from the previous setup as far as how things line up, then the problem may actually be the bases. Otherwise it's likely another issue.
If you do find that it's a base problem which likely needs shimming, don't try the mismatched rings you've considered. Take the earlier suggestion to use burris rings with their insert system. This will allow you to accomplish the same results as shimming the bases without damaging the scope.
