There are several things that can cause vertical stringing- barrel harmonics, barrel bedding, powder charge, type/brand of powder, cap brand, lighting conditions, sights on the gun, and how you hold the gun. Also up for the culprit, wind, fouling and fouling mitigation, bullet weight.
We'll look at powder and sights first-
Yes, brand of powder and how you dispense it really does matter. I can change the charge level just 2g on my percussion Sharps and move the group 2in vertical. Weigh your charges and use a quality powder like Swiss or Old E to eliminate this variable. Regular Goex, Reenactor Goex or standard Schuetzen may be at fault, but I'd say how you measure it may be at fault.
Sights- buckhorn and bead are not the best sights for accuracy. When the front bead covers 8+moa, there is no way in the world you're going to be accurate and add in the buckhorn and buh bye accuracy. If you have post and notch, glare off the top of the front post will absolutely cause vertical strings. To eliminate this variable, try some Sight Black first. If that works, then invest in a RayVinn smoker to blacken the sights with carbon soot.