Since the GH4 sports a m4/3 mount, you can adapt just about anything to that camera. That being said, I think some of the best options have been covered here already. The Panasonic 12-35 and 35-100, if you have the money, should be IMO your first lenses. Yes, they might be a bit too sharp for some, but dial down your in-camera sharpness and contract a bit in camera and you can get them looking cinematic enough. The constant aperture and OIS is also a huge win for those lenses, and turns the GH4 into a run 'n gun beast.
If you're not heavily invested in either Nikon on Canon glass, I would give the Voigtlanders a good look. Sure, they're not as 'future proof', because they're only native to m4/3, but they help produce some of the most beautiful and cinematic images off the GH4 I've seen. You can go the Speedbooster route as well, but with the Voigtlander you feel like you're not Frankensteining glass-on-glass-on-glass (don't forget your filters!), just using something that was perfectly made for the camera. Not to mention lighter!
Anyway, hope that long-winded answer helps you out :)
Also sounds like with the CAME you can't really tune the PID settings, what Dave Dugdale refers to as the plug-n-play Mac/Apple approach.
From the looks of it, Premiere didn't crash even once! :) In all seriousness, this is an awesome approach to constructing an efficient timeline - I think Larry Jordan also covers this in some of his tutorials. 3 day turnaround on that edit is also pretty darn impressive!
The real question is when the Metabones, speedboosted version of this product will be available. Would be a killer accessory for the GH4.