Hi Jim! I just sent an MG to Bob Naess via USPS Priority Mail and had no issues. Now, I sent as a dealer to another dealer and with a PS 1508 form, but I had no issues. They didn't ask any questions or scrutinize anything, they just took my paperwork and off it went, so I don't even think they knew it was C3. If I recall, you have a C&R FFL. Were you using that? I would think that would cover you, at least if it was a C&R sub.
In general, Buddy is right. Without a license, you can ship long guns as long as it is going to a dealer, but they will not ship handguns in the mail unless it is dealer to dealer.(18 U.S.C. 1715, 922(a)(5) and 922 (a)(2)(A); 27 CFR 478.31)
NFA can get a little tricky. SBS and SBRs CANNOT ship via USPS by individuals because the PS considers them to be pistols. The problem with sub guns, since many have barrels that are less than 16'' or have an overall length less than 26'' is that the PS can and will sometimes classify those as pistols as well. In other words, the PS has their own definitions for firearms that differ from what we encounter elsewhere. I have not heard about any rule changes, and it sounds like the ATF's advice was unhelpful. Sometimes, you just have to politely educate the postal folks. Their default when they don't know is to say no, it seems. Don't take no for an answer. Other than that, USPS has long been a preferred way to ship NFA. FedEx will ship NFA. UPS will NOT ship.
I guess the other thing you COULD do, although it is unnecessary, is get an ATF Form 5 submitted, signed and returned for your repair. That might help if this is consistently a problem. Kind of hard for them to shoot you down if the ATF has signed off on the move for repair purposes.