Hey everyone - my daughter and her little fingers took out the ashtray sleeve while she was sitting in the car the other day and pushed the small gear that is in the roof of the assembly up and into the outer "box" of the ashtray/cigarette lighter assembly. Now the door won't close because the piece(s) are stuck behind/under the door.

I figured I could access the thing from above, but now I'm stuck and haven't yet gotten the assembly out! Can anyone tell me how to proceed from here? I just need to pull the assembly from the dash, but it seems to be well attached still.
I have included a photo of where I am at this point. Any and all advice is very welcome! Come to my rescue, please.