John,
Overkill and in my opinion, it's useless! Why? For starter, as Jamie asked: who will administor this test? Then the questions will follow:
Who are these people?
What are their credential?
Certified by who?
Qualification?
Back to square one, you then still have to PROVE that the test was done for you, you were there at the test site, the polygraph result can be proved and certified by who?
Now you need backup evidence to back up that polygraph result.
Plus, as a wanna-be CO, I wouldn't even care if you give a polygraph or not. More likely, I will scruitinize your case even more so than before, "is he trying to hide something, normally, not everyone submits a polygraph test result?" Trust them to find dirts and flaws in your case if they really look for them.
Your response "it's hard to think like a CO" is true.... but that's why you have all these times (3-5) months typically to prepare your case, to think and role-playing your case with your wife and your VJ family

It's not that hard John, put yourself in the CO's shoes, and think if I show up at your house saying: John, I really need your approval to borrow your car for a cross-country trip. What will you ask me and want me to show you that I will actually drive your case accross country and not trying to use your car in a drug-smuggling deal? Samething here, the CO's job is to hear your case and be convinced by you and your fiance. He doesn't have to do anything and NO, he doesn't OWE you or your fiance a dawn thing. You want what he has

It's your job to ASK nicely and hope he likes what he hears and sees. Or else, send your case back to the US, start it over! Anh Map mentioned previously!
My vote: no polygraph, instead focus on getting the evidence you ALREADY have and prove to them this is an ON-GOING relationship! Not just a one-night-stand!!!! How? Only you can answer that question....
Good luck
chuck and kim