How do I get the transparency gradient to apply to the stroke?

Nice artwork.  There is so much going on, I have a very strong feeling that I am not understanding what you are trying achieve?  I initially took 'transparent gradient' to mean that the stroke faded away from the subject, which is better done with outer glow.

Now I am thinking you mean as below.  The two red circles are the same, with one having a white stroke, which, as you said, is not working.

If you are after the following effect

Add the stroke

Make the layer a Smart Object

Add layer mask and run the gradient.

Having now answered every question _except_ the one you actually asked, I'd better let you explain so we can try again.

Not sure what exactly you want to achieve. Perhaps Layer Mask Hides Effects from Layer Style dialogue can solve your problem?