I'm pretty surprised they told you to make the reservation yourself and call back. I've used those free night certs plenty of times in the past and each time I called Marriott to make the reservation without incident. They never once said I had to make it myself and then call back to get it changed.
Sounds like pretty poor service all around, but seems like it could have been avoided if the associate on the phone attempted to make the reservation for you and found out there were no award rooms available...
I concur with Versel. Every time I've called to use a free night certificate they've done the work. The hotels frankly do not know how to handle VISA certificates. I'd call your MR line number and request it once again. If the person can't help, ask for a supervisor.