I think you have overlooked a key feature of the Resort Availability Tool. When the Tool shows "Limited Availability", you can click on the Accommodation Type (Deluxe Studio, etc.) and the Tool will display a calendar that shows the specific days available or unavailable. The calendar will show availability for the entire month, the preceding month, and the succeeding month, not just the particular timeframe you were checking.
Give it another try and you might find the Resort Availability Tool is quite useful.