I'm using a Pacific Tool reamer that was used once when I got it. Other top gunsmiths use Manson reamers. Each has their following.
Mil-Spec reamers are available thru a rental program online (can't remember brand).
EDIT: https://www.reamerrentals.com/ProductDetails.asp?ProductCode=50BMG.s
My reamer is ground specifically for a Match Chamber (0.5540" neck dia) with Hornady Amax needs. I have used solid brass projectiles with great results - multiple 4" & 6" 5-shot groups at 1000 yards during FCSA competitions.
I have cut 7 chambers and it is in need of a re-grind after cutting a heat-checked SS barrel that was set back 4".
My reamers has multiple bushings on nose to match to a correct diameter of barrel bore.
I setup my LeBlond tool room lathe with coolant thru spindle and barrel. This made chambering very easy - done in 2 extended cuts. You can see the chips being flushed out flutes of reamer, assuring you are maintaining a consistent tool pressure while cutting. Finish of final chamber was very nice, no sanding or honing required.