Then you're all going to die inhaling that sweet sweet co2.
Talk to a gas fitter/plumber about ventless gas devices and see what they say.
Your first statement is complete nonsense. The second statement - the best plumber I know has a pretty large ventless space heater in a great room addition he put on his house. When they use that room in the winter, they turn it on and keep it quite comfortable. If you read what I posted above, I would not recommend a ventless heater in a very well sealed home - homes built in the past decade or so. But in older homes, there's a lot of air coming in from the outside. Also, ventless heaters have oxygen depletion sensors. While these aren't perfect and don't account for certain situations, such situations are all easily generally easily observable by the user. In this area of the country, a LOT of people use them to increase comfort in a room such as a living room. I don't think they're supposed to be installed in bedrooms. And, some place where they'd be used occasionally, but the rooms are otherwise unused, such as a basement, are great places. As the OP has forced air, in the winter time, those homes tend to have less moisture in the air than other types of heat - so, while excess water vapor produced can be an issue if the ventless heater is used continuously, this partially mitigates that.
I searched for stats - CDC had some older stats from the early 90's - around 13 million adults used ventless heaters at some point during whichever year that is. The number of people using them has increased as more states dropped regulations prohibiting them. And, CPSC reports that in 2009, out of all those millions of people, there were 2 associated deaths from natural gas ventless heaters.
https://www.cpsc.gov//PageFiles/136146/co12.pdf
Since the OP's basement is too cold when the house is heated to normal levels, and it's single zone, it stands to reason that he would be wasting a ton of energy in the rest of the house in order to warm the basement. Another alternative would be to add an electric space heater or two. If he goes that route - ignore all the fancy marketing crap. E.g., the miraculous Amish electric fireplace that'll save a ton of money. That marketing is complete b.s. When it comes to heat, a watt is a watt is a watt. The only difference would be if there were an infrared heater aimed at the OP, but for heating the space, every 1500 watt heater is, more or less, equivalent. There are arguments for and against certain types - "I like my oil filled heater, because after I turn it off, it keeps the room warm for a while." That would be the recency effect - they forget that it took that amount of time for it to start warming up in the first place. A $20 1500 watt heater does just as good a job as a $200 1500 watt electric heater.