The websites are often not totally accurate. And, if the entire stay is not available in the same accommodation, it will say there isn’t availability, when in reality there may be options especially if you would not mind switching to a different casita or villa during the stay if necessary.
If the problem is just with the first day, or the very end, you could always just have a stopover at The Peninsula Manila or elsewhere as a fallback. And availability could open up for you if there are cancellations or changes.