Of course right after I post, I figure it out :)
So to anyone else looking to do the same, it's well worth it. The key was the wiring was wrong. With an EMG H4 (or I would suppose any passive EMG), the wiring for the Shuriken is:
Black and white - solder together and tape off (don't connect)
Bare - tape off (don't connect)
Red (hot wire) - solder to W10
Green - solder to W7
The key for me was figuring out the the red was the hot wire (used this diagram for the clue: https://www.emgpickups.com/pub/media/Mageants/h/z/hz_h3_h4_b245_0230-0221rf.pdf)
It's sounding amazing. Much more alive and sounds pretty much like a standard active EMG 81 (which is what I was going for). So now this guitar really is the best of both worlds - the high output and powerful sound of the EMG and, well, all the rest of the guitars via the Variax system :)
A little trouble to get right, but worth it.
Hope this helps someone!