Well it would appear the issue is solved.

To anyone who might suffer this confusion in the future:

Greenman Gaming sells Windows copies of the game.
For whatever reason; attempting to purchase a windows copy of Heavensward off the Enix store was incompatible.
I've gotten word back from my help ticket that the issue was resolved.

Attempted to re-add the Heavensward key to my account; and it now works!

My thanks for attempting to help, Legion88; but I covered the steam / nonsteam issue in the original post.
This appears to have been an internal problem of some kind that I'm lucky enough for SE to have resolved.