After you get the crosshairs re-centered, a better mounting system and it's bore sighted (if possible), try this scope sighting technique:
Mount the rifle solidly with a mount and/or sandbags, etc. Put the crosshairs on the bullseye and fire one shot. Use a bright marker, bright tape, etc. to mark the impact point. Then remount the rifle solidly with the cross hairs centered on the bullseye. Important: The rifle must not move!
Now, with the rifle solidly set in place and the crosshairs on the bullseye, look thru the scope and without moving the rifle, move the crosshairs onto the impact point.
If you were able to move the crosshairs without moving the rifle, the bullet will hit under the crosshairs for whatever range you just sighted it for. I've used this technique for all kinds of rifles in all kinds of calibers. For those types that can not be bore sighted first, I'll do it one time at close ranges and then move the target to the normal range. Normally, the rifle is perfectly sighted with just one shot (Assuming good scope & mounts, etc) Hope this helps. Keep yer powder dry, Mac.
Tuff-Gun Finishes. The Name Says It All.
Mac's Shootin' Irons
http://www.shootiniron.com