Venice is awesome in your own boat. We did it in 2013 and it was the highlight of the adriatic
There are places you can anchor
in the lagoon
north and south of Venice proper and the marinas to the north of the grand entrance (on the inside of the sand spit) are not too busy - great sunset views over venice and away from the maddening crowds via vaporetto. Downtown marinas very busy - wouldnt bother trying.
We were there in late June and didnt have a problem getting a berth for our cat which is always harder than a mono. Agree the later you go the less boats most likely as the hordes that headed back south with us in July surely had to be emptying some marinas somewhere!
They apparently have a fireworks show around 20 something July which Im told is worth sticking around for but was too late for us. Apparently there are areas in the lagoon
you can anchor
for the show which sounds pretty amazing.