Commercial refinishers don't bother. I thought of using rubber stoppers or wood plugs but have not been doing barrels, anyway. Some said the heated air inside the barrel would blow out stoppers. Well the solution does not have to be boiling, it can work at like 160 degrees. I always use a thermometer and try to keep the solution between 160 to 175 and regulate the heat. I can see stoppers surviving 10-15 min. in that hot of water/park. solution. Just wonder if the seal is good enough with stoppers to keep out the solution anyway. Any kind of more durable substance you use as a stopper, is gonna be hard to remove afterwards.
Your gun is like your nose, it is just wrong for someone else to pick it for you!