Verticle stringing is a real bug-a-boo for me. I've had the problem often and believe there are a number of things that may cause it.

1. Variance in seating pressure.
2. Slight variance in bullet diameter so some are tighter in the bore than others.
3. Variance in how tight the gun is held, either with the hand on the foreend or the pull against the shoulder.
4. When shooting from a rest, variance in where the foreend is placed on the rest.
5. Sometimes the powder charge does seem to make a difference, and upping the charge a little improves the situation.