That one you're going to have to get advice from more experienced Marriott folk than me.
But - if I recall correctly.. You already have the certs in hand. Right now you know the Marriott O'Hare Suites is available. Make a reservation there telling toll-free # you're using the certs (check on the cancel by date, which is probably 4pm DOA) so you know you'll have a place to stay no matter what. You don't turn over the certs until you arrive.
Then keep checking on availability for the Courtyard & Residence Inn downtown every day or every couple of days until it gets closer. If it doesn't open up, try the begging thing w/ the res mgr a few days beforehand. If either of those work, then cancel the Suites.
I'm not sure comparing Easter & Memorial Weekend is an apples to oranges. More people stay w/ family on an holiday like Easter so something might open up now; MW folk may travel & stay at hotel. Just a guess.
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Sharon