I also shoot NSSA. From what you're saying about the sizing of the minies, your bore is NOT .577 if you're able to get a minie that drops from the mold at .580 in the barrel.
Here's the straight scoop, take it or not. Nearly ALL of the repops have differing bore sizes and some differ depending on where in the bore you measure. Get a range of pin gauges, they're not expensive, or get a machinist to check the size of your bore. For best accuracy, this is the first step. Next, get minies that are sized .001-.002 under your bore size. To do that, best way is get a mold that drops a bullet at or just above your bore size, and then pass it through a sizing die to get an absolutely concentric bullet with a known consistent size. Just because Lyman or Lee says a mold is X doesn't make it so, only testing will yield the true size. Both of my Colt Contracts have .580 bores. I cast a Rapine Trashcan and Hogdon minie at .580. I size to .579. Point to using a sizer is to uniform the concentricity of the bullet because the mold that is perfectly round hasn't been made yet and to insure the size is just under bore. Key is to cast over bore size, squeeze in a sizer die to just under. Sizers run about $35 and you can use them in an arbor press with a dowel or get ones like I'm using that fit a standard 7/8x14 thread in a single stage reloading press.
Next, lube is critical to success. AVOID anything that is a petroleum derivative as it will aggravate the fouling issue. Lots of folks run a mix of crisco/beewax/olive oil with great success. I use a lube that is sold at our home range called Lens Lube on my Trashcans and both of the Colts will stack the trashcan bullets into one big hole at 50yds and I can shoot 20+shots before even beginning to feel some fouling crunchiness. The Hogdons however, don't shoot nearly as well with Lens as with plain crisco, go figure. Point here is you have to experiment. I've had success with MCM lube as well. It's available from Northeast Trader. His link is on the NSSA home page under Links/Sutlers.
Powder- not all black powder is equal. Just as during the War, powder is made in differing grades and I don't mean "f"s. In our modern arms, plain red can Goex is ok but there is much better available. Don't get caught up in price. Swiss is about the best going with Old Eynsford running a close second. Schutzen has a rep of burning quite dirty. You will see accuracy differences between types and "f"s and only experimenting and keeping records of the results will tell what your gun likes. As for caps, RWS only. CCI reenactor ones might ignite it, but are very inconsistent for accuracy purposes. Let's face it, reenactors are only shooting blanks. Charge levels, from what I've observed, with 3f, best accuracy is about 60% of service charge. Some guns like 2f v 3f, you have to experiment.
Lead- wheel weights a big NO NO. Use pure, dead soft lead. I get mine from a local salvage yard where contractors who remove it from operating rooms and xray labs dispose of it. Usually it's sold at spot price, like about $.91/lb.
So where does this leave us? Well, my 1st Gen Parker Hale 2 band- bullet 579 Hogdon pure lead (sized from 580), 43gr 3f Old Eynsford, crisco lube filling the large ring and just a smidge in the base, RWS caps. At 100yds will put 10 shots into about 3 inches. On my Colt Contract 2 band, same load, about 4 inches. My musketoon- Parker Hale with Whitacre match barrel- bullet 576 Hogdon pure lead, 42gr Old Eynsford, crisco lube filling large ring and smidge in the base, RWS caps. At 100yds will shoot about 4 inches.
All of the aforementioned guns will run 10+shot strings with no fouling issues or drop off of accuracy. Cleaning is with Windex patches followed by Ballistol patches followed by a conventional oil patch and of course, cleaning out the flash channel and nipple. Before shooting, I dry patch the bore to remove as much oil as possible and fire at least 3-4 caps before loading to insure a dry bore.
Just as you established your bona fides, here's mine. I have built multiple rifles, AKs, FALs, ARs, etc, was very active in 3gun, IDPA, IHMSA, NRA HP and dabbled in the current precision rifle fad. I've also been hand loading for about 40 years. Most of what I learned in all that stuff, pretty much didn't apply to black powder, it's an animal all unto itself. The only commonality is methodology of experimentation, control variables, record, adjust, repeat. And, shooting technique is critical to success. If you can shoot one of these critters offhand well, you'll be a rock star with an AR. All told, I wish I had started first in NSSA, it's been a great ride learning how to make these guns shoot well and it's a blast to compete in. No other format has been this much fun.