If the stringing showed up fairly suddenly, and was not evident with other charge weights and/or powders, I think I would rule out the bedding issue for the time being. I have had vertical stringing show up before, and either an increase in powder charge or a decrease generally eliminated it. A change in powder may eliminate it as well. If you are at the max charge for the powder/bullet combo you are trying, it may not be safe to try an increase in charge weight. Your gun and temps. will let you know. A change in powder may be your best bet if you are not satisfied with velocities/groups achieved prior to the stringing.