I had a lovely (arguably my best luxury-property) stay at the Villa Milocer late last year. I'm surprised to find this post because it sounds like a nightmare. Still, I can empathize and feel concerned because under your circumstances, I'd certainly share in your disappointment.
I think it would have been fair of them to warn you not to stay on that particular date. This was something they did for me when I originally booked on a particularly rainy period.
Also, should you have insisted on pushing through, it's expected of them being Aman (and not "merely" a 4S) to suggest a list of alternative activities or provide you with earplugs or noise-canceling headphones.
At any rate, I agree that more is to be expected from an Aman. Please don't be put off though because this sounds more like a fluke. My stays with them have been flawless with "problems" only being that pizza in one is "excellent" while only "almost excellent" in another... happy problems indeed! Once it's done properly, you'll never want to check-in anywhere else.