I worked on this a bit yesterday. Here is the first test piece. It fit a bit too tight, so I'm fixing that. But, I think it'll work out quite nice. This piece now mounts on the side of the dash piece, not on the glove box door. There will be switch actuator that mounts on the glove box door that is basically an arm that pushes the switch.
Here is an updated version that should fit better.
And, here is the switch actuator. The block on the side is what will push against the switch. This piece mounts on the glove box door.