I understand now that what you are after is not going to work. This is not going to work, yes you are correct in that. Even the “angle morphs” and joint deformers within the skin modifier will not work with FBX this is strange but true. The perfect workaround for this that we all use traditionally unfortunately will not work here unless skin itself is smart enough to recognize the changes to apply to FBX.
Right now the only solution available is to copy the mesh and make the changes under skin while eyeballing those changes on the deformed mesh hence the target as reference, its not perfect but its the only one that is working since the morph targets would work then as expected. If you look past the awkwardness and have to deliver a result regardless of the way it’s done then this may be your only answer.
If you wish to mirror the result as you may expect to do then you can also but it is also a workaround using “skinwrap”.
I will keep a look out for a better method but so far all other tests have not been successful in exporting the correctives in a traditional way, I am curious as to what blender is doing, I can look into that soon.
Edit: I had to try on a extreme sample to realise some more of the differences while trying the other method. The fact that I was using voxel deformations" with extension 1 of max 2016 didnt help me realise the corrective was at 50% only in my previous sample. My bad there.