Paper patching is just different. Not necessarily better or worse. There are advantages and disadvantages, but it is almost the only thing I shoot. Almost.
In working up a load for a gun like this, I would start with wiping between every shot. This seems tedious but goes pretty fast if you get used to it. This will show you the best accuracy your gun is capable of (eventually), and once you know that, you can work with overcoming fouling - which is the only real challenge with using black powder. I wipe with two damp patches and one dry - however, for grease grooves that is probably overkil and one damp patch, maybe two will suffice with a better cleaning every 3 or 4 loads. I use straight tap or crick water for wiping and cleaning. No other solvents needed.
With a grease groove, I would not use a grease cookie if I could avoid it, so grease only in the grooves. What lube did you use? I assume that TC lube, which is probably not ideal, but better than Alox or other smokeless lubes.
Did you drop tube your powder into the case or vibrate it? And what sort of compression? OE generally likes a fair bit of compression ( 0.125-0.3" but more or less may be better). Never compress with a bullet. Either make a dummy cylinder to put into your case for compression in place of the bullet or make or buy a compression die (buffaloarms.com).
I generally recommend CCI-BR2 primers. Not a super critical thing, but these seem to always do well, if not best.
Paper patching opens up a lot of options. My rifles generally use a bullet that, after patching, is land diameter. This is the standard for target rifles. They also use paper that, with two wraps, make a paper layer that is about as thick as the rifling is deep. Some hunting rifles use bullets that under bore diameter (when patched) by as much as 0.004". Some - maybe most historically - were tapered (this is why I'm so interested in the "Dis-assembly..." thread). Currently, I'm working with a 2-diameter bullet to use in a vintage Marlin .45-70 lever gun. For hunting guns I use a slightly thicker paper, but that may not always be necessary. I have also used groove-diameter paper-patched bullets but these are my least favorite by a long shot. Paper patched will avoid leading if done right and they can greatly increase your powder capacity - not really an issue for you. But they are tougher to shoot over fouling. In other words, there are many ways to go.
I used to have a percussion double (18 bore Joseph Lang) which I spent quite a bit of time trying to regulate from the bench. It was not easy work. Doubles don't seem to be regulated for bench shooting. That is my only experience with regulating a double.