I did a quick google search. Butane produces nitrogen dioxide, a poisonous gas. And according to the internet, Butane is heavier than air and sinks. Natural gas is lighter than air not Butane. According to the internet
I'm having a tough time believing this. There's no nitrogen in butane or in oxygen. Are you saying that burning butane C2H6 with O2 somehow rips apart an N2 from the atmosphere? If anything, I always though nitrogen has a cooling and oxygen-diluting effect and nothing more.
EDIT: I just did some googling. It looks like burning methane DOES grab nitrogen from the air. Learned something new. Thanks.
For the Original Poster (OP): clothes, blankets, a thermos from home. Also, maybe you can get a cheap, off-season slip if you agree that everything is at your own risk. The risks won't be worse than being at a mooring. You could also get a $25 watthour meter and pay them for the electricity that you do use. At about 25 cents a kilowatthour, and with a radiator-looking space heater, you'll have a warm boat for an evening for about a buck.
I run my stove and oven on the boat, when working on her in the winter and when underway. The stove with nothing over the burners set off the CO detector once. I don't know if using a pot over the burner would set it off or not. The oven doesn't set it off, probably because the confined space in the oven makes for better combustion. So now I pretty much just run the oven. I make cookies too. Carbon Dioxide kills you after making you drowsey. It's not something to take lightly.
Regardless, the CO detector was mandated a few years ago by my insurance company. Its one of the best things I've gotten. It's wired into the main switch, so it's always on when I'm aboard. I'm thinking about putting a second one in. (And I heard they have to be replaced every few years.)
I'd go with the warm clothes and a thermos. Or get a part time job helping out at a marina. They might make you a deal then. You've bitten off a lot to chew. Good luck, stay alive.