OK! The coin arrived in the mail today, so my whole family jumped in the car, and we went to Harlan Berk to get it looked at. A few guys looked at it, and they were confident about it being real. It is struck at least three times, possibly four. I decided to leave it there so they could send it on to PCGS. I am afraid that my next update will be in a couple of months. It depends on how long it takes them to grade it. The last digit is definitely a "3," so it is either a 1923 or 1913. Under a scope, I am pretty sure it is a 1913 type 2. I'll see what PCGS thinks. They are always showing me fascinating coins, so it was fun to bring something in that got them all excited for a change.
Based on the braid, I think your guess is probably right. It’ll be fun to see what PCGS comes back with.
Search Heritage archives for "buffalo nickel double struck" and quite a few of them come up. Many of them sold well into 4 figures. Keep us posted and I hope you get a good result. I don't recall ever seeing a counterfeit double struck (or more) rotated in collar on forums, but I've seen some fake off center Morgans.