The mist is sort of a light source. So no matter what you do, you will not be able to use it with alpha or transparency, not because of any alpha format issues, but because of physics. Emission needs to be added, not mixed in to an image. You can add volume passes together in the Compositor and output them to a file in any format with File Output node. It should not be transparent, but should be added during compositing.
If you use PNG format, you will have an image that has color management transforms applied to it so it will likely go through filmic and sRGB transforms depending on your color management settings and that makes the color values not linear, which means even if you add it while compositing those PNGs in non-linear color space, the result will be incorrect and might differ from your expectations. Compositing is done with linear color, so it doesn't matter if you like it or not (doesn't even matter how hard you are going to press that down-vote button :D ), EXR is the way to go here.
If you absolutely need to do this with PNG, this should be considered artistic process keeping in mind that the workflow is completely flawed and the best thing to do would probably be concentrating on the visual look, so you might need to adjust color and density unrealistically if you need more or less of it. What you use for alpha in that situation makes little difference - the result is going to be wrong in any case. You might as well use the combined volume passes themselves as alpha since the brighter the mist the better it is visible (but again - that's just wrong).