The Thompson Center hawkins might have the old style frizzen and hammer. When you are at half cock does the flint point at the center of the frizzen or the upper 1/3rd? If it is more to the center, that is the old style. They will still fire but the new style is much better. Also make sure that the flint is the correct distance from the frizzen. I was shooting mine today and as soon as that flint starts to wear down, the rifle misfires...
Also you said,
I have had trouble getting to fire after cleaning and drying
. I am wondering if your leaving water or fluids near the vent hole or in the wrong place. I have a T/C .50 caliber Hawkins. I swab and clean with pure alcohol. Then wipe it with a dry patch. I think 80-90 grains of Goex FFg would not be all that out of line in the .54 caliber with a patched roundball. Use goex as your main powder charge of course and goex 4f as the pan charge (but of course I am sure you know that).
You might want to call Thompson Center arms and discuss the rifle with them. I am sure they will have suggestions as to how to fix the problem. With my flinter, they had me mail in the old lock and replaced it with a brand new one... This is now a sweet shooting rifle...
good luck with your rifle... There are others who know a lot more about this then I do...