Did you lap the bottom of the rings before placing the scope? It's really a good idea to prevent scope damage.
I like to bore-sight rifles the original way, by placing the rifle in a padded vise and looking through the bore, aligning it with a target at 100 yards, then adjusting the scope to coincide with the bore.
I have a setup at 50' in my basement workshop and can do a preliminary bore-sight at 50 feet. At that distance, the horizontal crosshair should be about 1 1/4" higher than the bore sighting target, provided the scope is mounted about 1 1/2" higher than the bore.
Laser bore-sighters don't seem to be as accurate as the old methods, at least the ones I've used. It's a fairly expensive one, touted as being the "most accurate", but had to adjust it by slightly bending the rod, but it still doesn't work great.
You shouldn't tighten scope screws without a torque wrench. Even "professionals" tend to over-torque them. That happened to a neighbor this week. They were so tight that the power adjustment ring wouldn't turn.