In my opinion, LB is spot-on, as usual.
I also would try a thicker patch - of course.
Natureboy - if thin patches produced good accuracy, the Friendship cross-stick buffalo target, chunk, plank and bench rest shooters would be using them too.
What consists as GOOD accuracy to the individual shooter, is what is important here.
Benched, a round ball gun of .50 cal or greater will shoot into 2" at 100yards - given good eyes & ability of the shooter. 3" is quite easy- with a good load.
Even offhand, you cannot expect to shoot a good target (what's good to you might not be to someone else) with inaccurate loads. Whatever group the load you use will shoot in the very best conditions as in near perfect rested conditions with you shooting, you can add that group size to the outside edges of the very best group you are capable of shooting offhand at the same range - with 'any' gun with iron sights - as that will show your potential grouping from the offhand position - with THAT load. You will never average tighter grouping than the load's capability PLUS your own.
I did a test on this very subject a few years back. The results showed conclusively that the more open grouping the capability of the load, the wider the offhand group that will be produced. In my tests, the overall offhand group was slightly larger than the 'formula' says it would be.
This not only happened in the test, it is completely logical that it would happen as well.
Discounting critical components, loading practices or load combinations and stating "It doesn't matter, I'm only shooting offhand" merely makes it easier for those who do pay attention to details and actually work to perfect their loads, to remain in the top shooter's group.
edited for clarity, I hope