This one doesn't sound clean. Given OP's mention of billing issues during his stay, it's more than likely that the authorization and debit are not synched. It's too late now, but best not to muck with credit issues during a stay unless you've got a good deal of excess credit lying around.
As a general matter, if you're a frequent business traveler, you probably want to have at least $15-20 K in excess credit at any given time.
Presuming that OP is credit worthy, if he needs access to the funds, he can ask Amex for a 30-day increase in his credit limit.