I have been on houseboat vacations every year in Tennessee for the last 20 years, and we run the gas generators non-stop for 5 days, and there are hardwired CO detectors in every room (6 bedrooms, 2 bath, 1 great room, 80'x18' houseboats). The alarms used to go off quite a bit, but we discovered this was caused by allowing a boat (or large floats, etc) to tie up next to the rear of the houseboat, that created just enough of a pocket to capture CO and get it sucked into the cabin. Now, it seems as long as we keep the windows closed and don't let anything near the rear side of the boat, we are good to go.
On my 320, I have yet to spend the night on the hook, but that day is coming soon, I will feel pretty comfortable leaving the gas generator on all night, I have 2 hard wired CO detectors, and one battery operated. I might purchase another battery operated just to provide some peace of mind to my wife.
My advice would be if you run your generator at night, be sure the side where the exhaust is, ensure it is clear and free to allow the CO to dissipate, and then ensure you have nothing open in the cabin, no windows, doors, etc, which might allow the CO to get into the cabin, triggering the alarm. I am not sure if this is valid advice, but that has worked for me so far. I believe CO is about the same density as air, so it will neither rise nor fall, so putting the CO detector anywhere in the cabin is valid, just don't cover it with anything.