hcanewannabe,
I'm in no position to advise you as to whether you should keep trying or just move on, but I do have some thoughts to offer.
It would appear that the false confession you made might not be considered permanently disqualifying; otherwise, there would have been little point in informing you that you could re-apply after one year. However, it is also possible that you were simply given a pro forma answer that did not take into consideration the specifics of your "confession."
You might consider re-evaluating the ethics of using polygraph countermeasures in light of all available evidence, including the unethical behavior of law enforcement agencies using an invalid test (as confirmed by the National Academy of Sciences) to judge your honesty and integrity. Does using countermeasures (while answering the relevant questions truthfully) to help minimize the risk that a
completely invalid test will wrongly victimize you a second time really compromise your integrity? (And if so, does it compromise it any more than your earlier decision to make a false written confession in response to your polygrapher's false accusation of deception?)
If, at the end of the day, you still feel that using countermeasures is unethical, what about the ethics of an employer that is willing to lie to and otherwise attempt to deceive you through the polygraph process (see Chapter 3 of
The Lie Behind the Lie Detector, for details) and then to pretend to judge your honesty based on junk science? Do you really want to work for such an employer?
You might wish to consider seeking employment with an agency that does not require pre-employment polygraph screening. Some states, such as Minnesota, New Jersey, and Massachusetts, outlaw the practice altogether. And some federal agencies, such as the
U.S. Marshals Service, do not rely on polygraph screening.
Whatever you decide, I wish you all the best.