Mike,
As I understand it, you and I have the same antenna motor. Here is my best recollection of what had to be done to open the motor and remove the broken piece.
On the 80 series, there is a hole in the right front inner fenderwell providing access to the motor. Remove the trim ring from the antenna. Remove any accessories blocking the access hole. Remove the 2 bolts holding the antenna motor to the inside of the fender.
From the cabin, gain access to the rear of the radio. (Sorry, can't help you here.) Find where the antenna cable plugs into the back of the radio. Remove. Use duct tape or something to attach a straightened coathanger to the antenna plug. (This is so you can easily retrieve the cable later.) Pull the antenna cable to give you about 3' of slack. You'll want the slack close to the PS firewall grommet where the antenna cable passes through the firewall.
From the engine bay, pull the slack through to the engine side. Now you should have enough slack to remove the antenna motor assembly and set it on something flat under the bonnet where you can work on it. Open the antenna motor (2 or 3 phillips screws if I remember) extract the broken piece, seal, and close the motor. Take note of the direction and position of the broken nylon gear. Reinstall the motor using the 2 bolts inside the fender.
From the cabin, pull the cable back through the firewall, plug to the rear of the radio, and reinstall. Put dash back together.
Now, you're ready to install the new mast. (This may be a '97 procedure) Have an assistant run up the antenna with the dash controls. All the way "up" (yes, there isn't a mast but the motor has to go up.) Shove the nylon ribbed feeder into the motor. I believe the ribbed side will face the rear of the vehicle. It will be obvious to you as you will remember which way it should go after you removed the broken piece from inside the motor. Have the assistant use the dash controls to run the antenna down as you feed the feeder and mast into the motor. Stop when the mast is completely in. Replace the trim ring and test. It may take a few up/down cycles for the motor and radio to remember the antenna position. Test by running it up about halfway with the radio on. Then turn off the radio. Antenna should fully retract. Turn on the radio; antenna should return to prior position.
Sorry for the rambling.
-B-