I do all my chambers with finishing reamer.
Since I use a high pressure flush system and ream at high speed I chamber with a finishing reamer. My barrels and reamers never even get warm. I am running 15 gallons of Rustlic 255R through my barrel under 10-125 psi. I cut .100 back out .020 let it flush, cut anther .100 and repeat the process. I pull out about twice during the entire operation checking for chips in the neck shoulder area. When I get to the last .050 I cut and flush about ever .010. Since I use a MARS I cut my pressure down cutting the final .050 but I check for chips every .010. This method prevents any chip rings in your chamber. It takes very little chamber polishing, chamfer the mouth and your done. I just did a .308 in a Broughton barrel Sunday. I ran my lathe in both directions at 600 rpms for 5 minutes in both directions warming the berrings. I dialed in the barrel with with .001 indicators off a tight fitting PT&G bushing and range rod. I dialed in the barrel until the needle was staying constant on a single tick mark. My lathe is proper aligned and level. I still use a floating reamer holder. I cut the chamber and inserted the same bushed range rod and put an intrepid .0001 indicator on it and another on the chamber wall just inside the tendon face. Both indicators showed less than .0002 TIR. Yes, 2 tenths. It can't get much better than that with a manual lathe due to bearing runout.