Unless one has connections, there is no meaningful appeal process for polygraph false positives with any federal agency. The best you can do to mitigate the damage caused by your polygraph operator's false accusation that you lied is to write a reply to the "better qualified applicant" letter you received explaining that you told the truth (and without offering any explanations or rationalizations for why you might have "failed"). Your letter should be added to your file and will document the fact that you didn't tacitly accept the accusation that you lied.

I hope you might consider contributing a statement about your polygraph experience for inclusion on our Personal Statements page (the 3rd one is mine):

https://antipolygraph.org/statements.shtml