The P3 fits in the cubby really neat (although it is a tightish fit) and the door is shut when not towing - I leave the controller in place and it just shows the Tekonsha screen when the van is not connected. I used double sided sticky tape under the bracket to stick it to the rubber mat and it stays in place no worries. Not all that hard to remove and you need to leave a bit of slack in the controller wiring to allow the plug to come clear of the cubby to make it easy to plug/unplug.
Now - to put the controller in the cubby I pulled it out......easy to drill the hole then.
There are instructions on removing interior trim here (and lots of other good stuff) http://www.wk2jeeps.com/wk2_interior_trim.htm
Looks scary but I didn't think it was all that hard. I took the view that the controller was there for the long term and I didn't want to compromise on the position.
Very important if you disconnect any wiring you do not turn on the ignition until everything is reconnected. Very tempting while testing but the Canbus will have issues if it runs a system test with disconnected wiring.
That's another reason to stay away from any Jeep wiring and install yours separately.