Develop and offer a low profile USB cable that will allow a power pack to connect to the iPhone and fit flush (or nearly so) with the Fjorden iPhone case.
There are some on Amazon
but there are complaints about not working with a cased phone.
Maybe have the wire from the phone turned 90 degrees from the one on Amazon so it is parallel to the back plane of the camera.
Should allow continued use of the Fjorden-grip equipped iPhone while recharging from a battery pack with minimal interferance.