This is what I use for my Thompson-Center TCR-87's. Such a device should work for any break-over single-shot (the other Thompson-Centers and the H&R's) where the barrel can be removed from the rest of the gun. My son-in-law built it for me. He probably got it done in an hour, but it would have taken me at least three times as long.
The cleaning rod is guided through the slot and the cleaning rod handle is cradled in the box that slides along the rails. I put a little wax on the rails and there is very little friction. I feel better knowing my barrels are not getting damaged while cleaning. It is a big apparatus but always goes to the rifle range with me when the TCR-87's go.
