First of all, everyone with the Hyatt Visa is now Platinum but only Diamonds get their free nights in suites. So that's a no-go.

In terms of the rooms on points, Hyatt allows you to book a suite with points for approx 50% additional. Short of that, while it is conceivable you could get lucky, don't set yourself up to be disappointed. You'll get a nice room unless you make other arrangements with the hotel. Why not find out if they will comp breakfast as part of the $300 per night suite fee?