I've stood exactly there myself, Santorini is a truly an amazing place.
But unlike you for me there were heaps of folk milling about the whole time for me. I ended up taking multiple shots and combining layers in PP to get the "no people" look.
I was also luckier with the weather, I know I know not much you could have done about that, apart from go back another time. But a bright sunny day gave me a bright white building and deep blue Med sky, which gave my shots a lot much more punch.
I also got a lot closer on the building itself, but hey, I like the dogs too.