No brilliant ideas, but although I like e-mail for many things, when there's a problem, I prefer to speak to a human being if possible (and then a supervisor, if needed), or go to the other extreme and send a real letter, with copies of all pertinent bills, etc.
A copy of your Amex statement should help Marriott fix this. The issue seems to be between Marriott and Amex, and the underlying problem could be coming from Amex. It shouldn't be your problem of course, but you may have to demonstrate to Marriott that you have paid Amex.
Believe me, AmEx's accounting department makes mistakes! This may NOT be the problem, but if you add a lost card into the same time frame, it seems possible.
Calling would be fast. You might be able to fax documentation in to Marriott and get your points reinstated pretty fast.
Otherwise, you have until 31 JULY to redeem the 200K award. That should be plenty of time to resolve the issue.
A letter to Corp couldn't hurt either.