I got a response from KGHobby. Only "Special Edition" is shipping now.
I investigated a bit and it appears Sideshow have an "Exclusive Edition" with that mini Emperor Holo figure. This has enabled them to somehow have first shipment. The "Collectors edition without hologram" and presumably all other shops (KG included) will come later apparantly. They mentioned another 4-6 weeks. Which sucks.
So yes, we'll get the "Second Batch" once they've ironed out all the production issues. Would be awesome if they changed the material on the robe. But I doubt it.