I am not sure if the reamer will contract Kooties if it touches a T/C barrel, only Tim can answer that one.
The same reamer will work.
Get your self some cutting oil of some sort and a T-handle (I used one from a tap & Die set). Oil up the reamer and start cutting by turning the cutter clockwise. putting some down pressure on it, but not a lot. It will cut a little at a time. I turned mine until the reamer almost touched the existing rim relief. Keep tuning it the same way and withdraw the reamer. Clean the camber, bore and reamer, put a light coating of oil back on the reamer.
Good Luck and Good Shooting