The same firm that specializes in the tiny compressors also builds larger bldc units. These ones run off r600a (butane lighter fuel):
H Series Catalogue -
The soda can line runs off r134a, it is commonly used in cars. If I wanted to use a natural gas in one, butane fuel would work. To get a decent condensing temp, some propane might need to be blended in. For such a small rig, I would probably just stick with r134a.
You won't see me messing with any of these things anytime soon. Until the end products start showing up in the second hand stores and yard sales, they are out of my target price range. For the price of a new compressor and control, I'm confident that I could throw together a mini split.