Recently, I purchased a very slightly used fluted barrel that was a button rifle barrel. I measured the bore dia with a PTG range rod and reamer bushings graduated in .0002 increments. The muzzle and breach end measured the same, while the area under the fluting opened up. The proper fitting pilot on the muzzle and breach end felt like it fell in a hole under the fluting. I was skeptical about even chambering it, but I thought it would make a great research project. I cut the threads off the back end and chambered the barrel for 260 AI. After about 10 trips to the rifle range, I realized that I had wasted enough money trying to make a bad barrel into a good one as I don't call the very best(occasional) 3/4" group accurate on a long-range barrel.
So, if you want to turn down a button rifle barrel, you take the chance on the inside bore dimension opening up giving you some very strange harmonics.