The N.S. bolts were Springfield and were never used (new or rebuilt) in the A3's. As far as the R and 32, I've seen them with numbers under the handle, but can only speculate on the R, it's definitely not Remington. Barrels were all selected from the same production run, nothing differentiated them until they were selected to go on an A4, they were air guaged, when they met acceptable results they got a punch under the end and went to the finishing process. I believe the punch mark was to let the front sight guy know not to put one on it (it was in the middle of the machines surface for the front sight).
I don't think your rifle was a drill rifle but it has been pimped, in addition to the other things pointed out, the front sight is aftermarket. Lyman I suspect, should say in very small letters on the side.
Check the bolt, take it out and check the bolt body for serial numbers, roll the extractor around and check from the bottom. If it has a 7 digit (not sure if they ever used 4) number neatly electropenciled and being polished it could have been out of a NM rifle. I will send you a PM.