I have a TC musket cap nipple for an inline I believe, which fits the H&R breechplug, and the forward end projects about 5/16'' beyond the threads.
Just try-fired a cap on my Huntsman, and it works perfectly. The ''tophats'' have about the same energy as the 209's, I'm told.
I don't have a part no. or anything, the things been rattling around in my muzzleloading parts & tools box for years, but I'm sure it's a TC item. Overall length is 15/16'' or so and thread is 1/4 x 28 tpi.
With the extended tip, which has center and side flash holes in it 'hot-shot' style and using musket primers, your misfires should be remedied, AND the "percussion" requirement in your home state would be satisfied.
I hope this will be helpful.
Look for replacement parts for the early model TC inlines, including aftermarket, as I believe that is what this item was specified for... I doubt it was meant for a traditional sidelock, the long tip wouldn't seem to be able to fit into the shallow bolster on those.