As long as it only works with HDRI, you could render your alpha channel as a greyscale HDRI.
Sidenote: 12k to 8k is a weird format for a cubemap o.O i would have expected either 12k to 6k or 16k to 8k, a 2:1 format.
The cubemaps or spherical panoramas i have dealt with are all in 2:1, like those things here:
Edit: … yeah, why not simply use a regular exr/jpg spherical cubemap and drag it on a sphere and make it two sided? ^.^ All that math is not required, if you use one of those with spheres. Then you also have no problem using the alpha, if you set the material to translucent.
So if you get an EXR, just make sure, that you get it as a spherical cubemap (or whatever they are called), thats the easiest way possible.