I don't know that I would ever use steel wool inside a barrel chamber. That is a risky proposition at best. If I did it would be the finest grade of steel wool I could find. A better solution in my estimation would be to use bronze wool that many hardware stores sell. I would soak the bronze wool in something like Kroil first and then go at the chamber. I wrap strands of real copper Chore Boy pads around a slightly worn bore brush to clean barrels and chambers. Just make sure the copper pads are not the copper washed style steel wool pads. If in doubt use a magnet to check. I don't use a drill for this.
For lesser fouled chambers and barrels I use VFG Intensive pellets for cleaning. No drill needed with these. Put some JB bore cleaner on the pellet and clean away with elbow grease. Follow up with JB bore polish on VFG Comfort pellet and it should get the job done. If the chamber is really crudded up you may have to do this procedure a couple of times, but you have no fear of doing any damage to leade, lands or groves.
I have also just started using a cleaning paste form a company called TCS Products. It has shown some really good results and you may want to give them a try. I like it better than the JB Bore cleaner I normally use.
650 FPS is too slow for your load, but I am happy to see you ran it thru a chronograph. Federal factory wadcutter ammunition ran 735 FPS in my M-52 and my handloads duplicate this speed with Hornady 148 HBWC bullets. I use WW231 or Solo 1000 which is no longer available. Solo 1000 was a very clean burning powder and it's too bad we can't get it anymore, but WW231 works well too. I never cared for Bullseye powder much at all. Good Luck!!
Rick H.