Many of us who had jobs working on GM products found we had many broken key removals. We had several hand made tools in our tool boxes for the job. First and fore most was some tiny needle nose pliers we filed down really thin, that takes experminting so they are not to thin.
Second was a asortment of dentel picks bent and filed thin. Most of the time that would work to reach in and get ahold of the broken key.
We also had fish hooks and mending needles.
A pair of sissors works on the pop corn that holds the door pad on. NO DON'T cut it just place the blades on each side and pry enough you can get your finges in there for a grip. A bigger set of needle nose plires will work too.
If you buy the tool to remove the window crank that works on the popcorn too.
Once the door pad is off there is either a paper or film barrier you have to peel away.
Peeking inside the door with the window up by the way you will see a two legged fork with the handle end turned up a bit. Insert a long screw driver or pry bar in between the fork handle and the lock and pry the fork back. The rod is held on by either a small metal clip or in the newer stuff a plastic clip, just reach in and gentle pull the retianer part up and twist the clip .
Once the lock is out you can try taping the broken part out,use a screw driver handle and tap on the back side of the upside down tumbler. Since there is no hole on the back side you can't push it out.
Not sure if the dealers will sell just one door lock or not but you can buy one from a salvage yard and have a lock smith key it like the other one.

Al