Just wanted to add a point of context. I worked at a DOD facility that signed a petition to decertify our union (ironically we were trying to remove the existing union so we could join NATCA). The petition goes up to an agency called the Federal Labor Relations Agency and that agency administers an election. As you can imagine in the current administration the FLRA, an agency which is almost entirely made up of labor lawyers, has probably been entirely canned by DOGE. Our petition got unanimous support (100% of controllers signed) and still our petition has been awaiting further updates from FLRA for over a year. I have since left the facility, as have about half the controllers who signed the petition, and there has still been no election.
So keep that in mind if you decide to pursue this. I would recommend using something like this to drive a point home and show NATCA that you are serious about fighting them unless they give in to your demands, but know that the actual process of decertification is painfully slow and will probably take all the steam out of your fight before it gets the finish line.
It would probably be more effective to draft up the petition, do a "straw poll" where you can know the number of BUEs who would be willing to support decertification, and then bring those numbers and petition to a NATCA convention with demands such as amendments you want in exchange for dropping the issue.