D2D,
You're mostly right although there are joint acknowledgements of other authority STC's. The FAA, as the original certifier, would want to first approve any STC and, once they have approved, any other authority like the CAA or EASA would then send in an inspection team to check all the paperwork over before issuing a CofA in their state of registry.
All the above ties in with info I've had that Premier, or something similar, were going for their own STC to allow 15 full pallet carriage. To achieve that, they would have to move the 1L door forward (the PF only has 1 door).
Be interesting to see what the weight penalty of moving the door & fitting a fixed bulkhead would be. The Boeing STC doesn't give as much payload as expected so any added weight would come straight off the payload.
RT