If I was going to shoot bullets out of a Thompson Center Seneca rifle, then I would give serious consideration to the following modifications. Especially, since the walnut is now so old, and unless you are the original owner, you have no idea what conditions of humidity that the rifle has been stored in prior to you owning it. And, even more especially, since the rifles were designed to be petite, with fairly small wrists to start with. Wrists that have a history of breaking on the regular when shooting loads with moderate-to-heavy charges of powder. And, that once broken, are VERY, VERY difficult to repair.
I would purchase from Track of the Wolf, PLUG-FH-16-3 ($40.95). This is the flint, hooked breech plug with a 5 7/8" long beavertail tang that has a face plate perforated to fit a hook exactly the same as the ones that T/C uses. You are purchasing it for the tang, keep the breech plug to sell/trade at a later date.
I would remove the factory tang/face plate, and inlet the stock for the longer beavertail tang. After first filing the octagon flats of the face plate from 1" to 15/16" across the flats. I would also purchase one of the long-bar Hawken doubleset triggers from TOW, such as TR-LR-1300 ($65.00), and inlet it into the stock so as to fire the lock properly.
Then, with 2-3 tang bolts connecting the beavertail tang to the trigger bar, the wrist would be significantly reinforced against virtually ever breaking. Then, either reuse the stock trigger guard, or purchase a more Hawken-like trigger guard to replace it.
The last thing I would do is to glass bed the recoil face of the tang, and the entirety of the barrel channel.
By the way, NICE SCORES on both the Seneca & the Patriot. The .36 caliber Patriot is a real find, as far fewer were made than in .45 caliber.