STOP DO NOT wrench down the rings till you can't tighten them anymore. That is a sure way to add that new scope to the junk pile.
If you do not have a torque wrench then get your screwdriver and hold it by your thumb and index finger only now go back and forth and tighten down each side the same amount till you can no longer turn the screwdriver with just the two fingers. That is plenty tight for a 30-06.
I forget the exact torque setting for rings but I am sure I can find it and a short video on how to do this.
If you really want to do it right get yourself one of these Wheeler Engineering FAT wrenches from midwayusa.com