You never know until you call. In general, weekends are easier to book at The Plaza than weekdays since the business travelers aren't there. Most NY hotels offer their "deals" for the weekends. Tourism is still off as well, so it may not be too difficult to book.
Here's a link the their website. A quick check shows availability for the weekend of October 11. I'm not sure how they work available inventory with DVC but I bet your chances are good.