I believe Amex closing your card versus you doing it makes no difference on your credit report, so I'd just go ahead and go through the FR unless you said you make $100,000 and only make $10,000 a year.
I was in the same boat as you were and made it through fine. I did fax in the trust fund I drew off of even though they said it would not factor into their decision.
This doesn't sound like an FR though if they haven't called you to inform you you'll need to fill out the 4506T form before you could use your cards again.