The security clearance process contains several steps, check Wikipedia for details, but the order of those steps may vary.  It will not start until you get a job offer, or a conditional job offer of employment
(COE).  Most government agencies like the CIA will first give you an interview with your prospective office and then issue a COE if the office likes you.  Then the security folks will step in and the polygraph is first, along with psych, medical, and drug testing, all over a 3 day period.  If you fail the poly, they don't even bother with the rest of the security clearance process.  You are rejected right there, COE rescinded, game over.  It is cheaper to polygraph applicants than to run the top secret background check. I hear the NSA may do the poly and background check concurrently.

If you apply for another job that requires a clearance, one of two things may happen.  They may have you fill out a pre-clearance survey as part of your initial job application to assure them you can get a clearance.  That survey may include a question like "have you ever had a security clearance/access revoked, suspended, or denied"?  You are to answer truthfully, and when you answer "yes", they will toss your application in the garbage.  No chance to explain yourself.  They want a candidate with no issues so they don't waste time and money on trying to clear someone who may not get cleared.

Or, they may interview you and hire you and make you sign a form that says you must get a security clearance within the first year on the job or your employment can be terminated.  So if you get hired, and you never get your clearance, and the security folks see that Incident Report (IR) from OGA in your file, they will ask you "What is taking so long? Is there something you wish to tell us about this IR".  After you explain yourself and the company/agency gets tired of waiting on your clearance to be adjudicated after a year, you are fired.  But at least you got a paycheck for a year!

An IR in your clearance file, whether from a failed polygraph or an arrest, when you are not currently employed with a job that needs a clearance, is a big red flag.  You are in a tough situation.  The IR cannot be adjudicated until some company/agency sponsors you for a job-needed clearance.  However, the catch is that not many companies/agencies want to waste money on sponsoring a prospective employee for a clearance who has an IR in his/her file because the company/agency does not know how severe that IR is or how long it will take to resolve!  You are now a reject in the national security community.  You are a red-headed-bastard-gay-stepchild that nobody wants.

You'll just have to seek and find one of the select few agencies/companies who will hire you and sponsor you for a clearance, despite the IR that the CIA put in your file because of the stupid polygraph.

I wonder if it's really worth all the treasure and time

wonder what would happen if, attached to the appeal, were a polygraph report, with charts from a qualified and recognized polygrapher, disputing the previous results?

violated my security clearance due process rights of right to a reasonable timely process. I don't expect to hear back from them at all. The CIA is filled with so much fear of W

I expect never to apply ever again for any clearance job with the Agency blacklist on you...even DoD or some other 3 letter agency.  Or even better...move out of the hypocritical DC area and start over.