if you do a search on here, you'll find a post I made about running a 6mm reamer in a .243 chamber. It won't clean up, and it seems like it leaves a five to eight thousandth step all the way around. the location of your ring is just about right (about 1.80" from the case head). To fix this, your going to have to do a barrel set back of at least a quarter inch, and I'd go three eighths inch to get you a nice clean throat. The other solution is to find a 6mm Ackley reamer, and simply clean it up with a one thread setback (incase the head space is also off a bit).
You can do a quick check to see if there is a step in the chamber with a straitened out paper clip that has a small upwards bend on one end. Just rub it on the chamber wall. If there's a step, you'll feel it. Of course you could also see it with a bore scope, if you have access to one.
gary