Sure...,
First, recover your patches and examine them very closely. Your Thompson Center is a 1:48 twist rate. It will, counter to some information that is based on manually rifled barrels, handle some hot loads, BUT going beyond 90 grains you are creating other factors.
(btw that load data was dropped a LOT lower in later manuals..., I wonder if your manual mentions double ball in a .45 caliber for deer? They did at one time)
[ok back to the thread]
So with that large a ball, you have a thinner patch than you would with a .530..., and with that large a powder load, you're probably simply blowing some of it out the barrel, AND you might be burning through the thin patch.
So try a .530 ball and a thicker patch. and no more than 90 grains in 3Fg..., you want the faster burn.
Next, reduce it even further and perhaps try .520 round ball
https://www.trackofthewolf.com/List/Item.aspx/127/1/BALL-520-X or
https://www.trackofthewolf.com/List/Item.aspx/127/1/BALL-520 and chamois for the patch (local auto parts store; get
real chamois). This will give you a lighter ball, with the faster powder, higher velocity. You could go even further and get a Lee .520 mold
https://www.trackofthewolf.com/Categories/PartDetail.aspx/1202/1/LEE-520-6C, and cast wheel weight alloy bullets in .520. That would give you probably the lightest roundball that you could accurately shoot, and with the highest velocity. I wouldn't go to all that trouble though unless I had some increased success with the pre-made .520.
IF you want to exceed 90 grains with that PRB, you're probably looking at an aftermarket barrel in a slow-twist, say 1:66 or even 1:72, and longer too, say at least 36". That's a bit of cash to consider
See part your problem is the extreme range. The round ball sheds energy very fast. With average loads of 60-80 grains the .490 and the .530 ball get very close to similar velocity at as close as 100 yards.
So instead of getting an aftermarket, longer barrel, probably custom fit to your rifle..., you first may want to consider a conical bullet. Remember, the venerable .45-70 Government (black powder) round launched a 405 grain bullet using 70 grains of compressed black powder..., at almost 1400 fps, and that can reach out and "ding" a target at 500 yards. Sure..., probably using a flip up rear sight, some good elevation, and lobbing it in, but the conical shape made better ballistics than a round ball. Back in the day they got even bigger for really long range. The .50-90 Sharps was reported to have been used by Billy Dixon at The Second Battle of Adobe Walls on the 27th of June, 1874, to make a 1538 yard shot.
So I'd try 70 grains of 3Fg, and try a 300 grain conical for the .54 in a REAL bullet
https://leeprecision.com/mold-d-c-54cal-300.html, and in a heavier, more traditional Minnie style
https://leeprecision.com/mold-540-415-m.html, and I'd begin out to 100 yards, and the one with the better group I'd use to try and reach out to touch the target at 500 yards..., adjusting the powder upwards if I felt it was needed. Again, remember that the 405 grain, .458 bullet launched with 70 grains from a .45-70 trap-door Springfield would get there, so one of those two bullets from your .54 should be closer than with the round ball. The lighter REAL bullet is going to be moving faster, but it's stubby compared to the Minnie at 415 grains, and I don't know if the shorter bullet will destabilize on its way to the 500 yard line. You'll have to experiment and see.
LD