I am running up against a poorly designed ceiling fan design.

Short version: I have a couple of bulbs stuck in my bedroom’s ceiling fan/lamp combo.  The problem is that the bulbs are set in those stupid cone things where you have to remove the bulb first before you can remove the cones.  This is a particular problem because the housings for the light sockets are no longer secured to the lamp itself anymore.  There’s no exposed wiring or fire hazard — I checked that, ya, you betcha — but when you turn the bulb it just twists the socket, so I can’t get the bulb out.  And I am reluctant to take some pliers to the socket housing to keep it stable while I somehow unscrew the bulb with a third hand or something, for obvious reasons.

Suggestions? I can’t be the first person that this has ever happened to.