Saw your post over at the NSSA board. The Lee Improved minie does not shoot well in any of my guns- 62 Colt Contract, PH 1st gen, PH musketoon, 62 Colt Sig Series. Not with any level powder charge nor with any lube that I currently use with great success on other minies. Another thought, I've seen some Armisports that won't shoot well regardless of what you do. Hopefully you don't have one of those. Examine the bedding/inletting to determine if the tang screw isn't torquing the barrel.
A couple comments here on accuracy with minies-
1) Large powder charges are NOT needed and in fact, may hinder accuracy. Minies aren't designed to shoot in deep cut rifling so you're wasting your time in guns that weren't designed from the start to shoot minies. A charge level of about 60-70% of the service charge of 60gr will nearly always yield best accuracy if the minie is suited to the gun/rifling.
2) The ONLY minie design from Lee that I've found to shoot well is their copy of the Rapine Trashcan. It looks like a gigantic wadcutter and it shoots as well as the Rapine when sized to the musket.
3) Experiment with other powders. 2f isn't the only thing you can shoot in a musket. In fact, my 3 band Colt really likes the RCBS 580213 with Lens Lube and 35g 3f Old Eynsford. All three of my 2 bands shoot better with 42g of the same powder and the Rapine Trashcan. Don't know why this is, but it is completely verifiable. Of the powder available, Swiss is best followed closely by Old Eynsford (Goex product). Testing will tell what works best for you but I don't know of any successful serious competitors who use anything else.
4) LUBE. Ask 5 NSSA members what's best, get 10 answers. Experiment. I've found the optimum lube varies with the gun in question. My PHs like the RCBS Hogdon with tall base plug lubed with 50/50 beeswax/lard. I tried Crisco in the mix, but it can't touch the lard mix, that was confirmed in a head to head test. The Colts don't shoot that minie well with any lube I've tried- yet. My 63 Sharps will cut one ragged hole at 50yd with the lard mix but nothing else so far tried will equal it.