Propane behaves very differently than LNG or CNG. Neither of those is heavier than air in gaseous form.

Refilling is going to be a very critical part of the puzzle. CNG can be "made" from the natural gas supply in your home with a relatively small compressor, I don't think that's an option for LNG, as the energy and equipment required make it impractical for home applications when your supply is very low pressure natural gas supply.