Pete,
I was also thinking of heading out there in the next few weeks, remembered your post and contacted the Town of Brookhaven which owns and manages that marina. Here is what they said:
1) The marina is currently in the process of being rebuilt, the boardwalk to the ocean is no longer there.
2) The bathrooms are not open, so there are no facilities. They added it is very rustic.
3) Boaters are more than welcome to tie up in the marina but at your own risk.
4) They do not anticipate the repairs will be completed until right before the 4th of July at best.
When I asked them about the condition of the channel leading into Great Gun they reached out to the local bay constable and said that the channel has been properly marked but could not give me any info if any debris had been removed from the boat basin in the marina.
I have decided that I will not being going to Great Gun. Hope the info helps.
--Steve