If you build the plywood lifting platform, I suspect the load would be spread very well over the floor joists.
I was in my basement, it was not working for the same reasons you mention, and moved to garage.
I have a kerosene heater, it sucks when you are sucking wind and tasting it. Luckily I am in Colorado where it is rarely needed. If I did not have a big garage, I would have cleaned an area to quickly deploy equipment, and move it to the side to park. A friend of mine has a gas fired (externally vented) garage heater...that is the bomb.