I made my own carbon chamber a few years back and its holding up great. When designing mine, I made a short carbon tube insert in the manifold end so that I could really get the coupler bands tight and not worry about crushing or distorting it. It sounds like if you are going to grind away any material inside the pipe, you could build an insert and epoxy it in. I found a cardboard tube near the size I needed and added painters tape until I reached the ID of the insert I needed. Then I put a layer of vac bag material over the tape before wrapping it with carbon fiber. Next wet the carbon fiber out with a high temp epoxy resin and wrap some bag material around that. stretch and wrap electrical tape around the bagging material to squeeze out the excess resin. After that cures for a day, unwrap and trim it. Get it to fit somewhat loosely in the end of your exhaust chamber, then remove it to post cure the part by cooking it in an oven / toaster oven per resin instructions. After that is done, you can use a high temp carbon paste to attach the carbon instert into the chamber and let it rip after it cures.
I know this sounds like a lot of work, but doing anything with carbon usually is. I don't think you'll just be able to smear some resin or paste in there and make it last. If you do try a quick fix, maybe jb weld or some type of devcon putty will hold up to some temperature.