Bigted, Thanks, That is where I always started when working with a problem like that. BE interesting to see how it is resolved. Just about the time you think you have BP cartridge figured out, it gets ya!
country gent, I have never shot a real gun at 1,000 yards, only 45-70 and 45-100. The matches only allowed a rest under your hand at 1,000 when I started. No rests at 800 or 900. No prone x-sticks, but some shot them setting up. I shot back rest. Most shot prone with a sling. Due to cataract implants, not being able to see the targets and recoil of the 550 gr slug over 90 grs of 2 F being a migraine trigger, I have drifted away for LR BP. Now my focus is 200 yd offhand schuetzen shooting.
Back to vertical stringing, my first LR 45-70 would do that over a string of 15 or 20 shots. After looking over my shot records, it was quite predictable. Turned out to be leading in the throat on that rifle collecting fouling and more lead. I was shooting duplex at the time. Way before blow tubes became fashionable.