Not a big deal. Closings are often at the mercy of processes beyond the control of the closing company, such as how long it takes the local government to record the deed. It's a much different process than where a local title company closes a home sale and walks the deed over to the registrar to be recorded on the spot.
Contact the closing company and give them instructions regarding mailing the losing documents to you and what they should tell Marriott for your correct mailing address. And if you haven't heard from Marriott by the time you move, contact them every few days until you are in the system to ensure that they have your new mailing address.
It may take a bit of extra work, but you can exert a lot of control to ensure this all goes well.