There are several points along the eastern shore of Great Harbour on Peter where I have seen yachts anchored though I have never anchored there and can't provide any personal experience. Looking a the charts and google maps it appears there is quite a bit of sand once you are off the reef that is up against the shoreline in what would be 10-20 feet of water. I'm sure someone here has some experience anchoring along that area and could provide some extra reassurance though.
I do love the seclusion and holding along the eastern shore of Little Harbour though as an alternative. I have day anchored in Deadman's Bay but it is likely not ideal for an overnight stay dependent on the prevailing wind at the time.
We haven't anchored there post-irma, but prior to that often anchored and never had any issues. Always very good holding.
There may be more mooring balls now which might change things, but if you cut and paste the following into google-maps it will show you roughly where we always aimed to drop the hook: 18.357095, -64.580042
Many thanks to you both...there are mooring balls there but when we went in October they were too close together. That southeast corner though was clear.