Anyone with experience using this service?
I recently purchased a 7D Mkii and I think it might be (not completely, but somewhat) a happy medium between the two cameras you mention based on your situation. I have shot with the 6D and GH4 and the GH4 is a clear winner between the two for video.
In the 7D Mkii you gain the Dual Pixel Autofocus, 60p at 1080, along with a few other video-friendly features.
I needed a camera for photography that could, in a pinch, deliver decent video results and I have been really happy with it. If you are needing something for stills, be aware that you lose autofocus capabilities with the Metabones adapter and your Canon glass on the GH4. It will produce a decent image but nailing focus is much more tricky.
So my recommendation is either wait till an eventual price drop on the GH4 or opt for the 7D Mkii in the mean time. I have seen the 7D Mkii on eBay for as little as $1,199 recently.