Get rid of that POS scope! I had a Simmons once, 3x-9x that would move POI an inch for every notch in the power change ring. Sent it back, and the replacement was WORSE! Never again...

If you have a boresighter, sometimes setting up the boresighter in the normal way, then adjusting the power ring back and forth, and moving the adjustments back and forth will indicate a scope failure. When the power ring is moved, if the crosshairs appear to move, the scope has failed. This is very common with the simmons scope with the red ring. If you do not have a boresighter, a local sporting goods shop will usually help with this.
Good luck with your project!

When my .375 went from shooting overlapping holes at 100 yards, to wandering all over the target, the problem was a loose action screw. Doh!

Savages _usually_ shoot great right out of the box.