Is the bellcrank broke off at the housing? Looking at the picture of the bellcrank on Mike's website it is shown upside down, The "T" actually points down and is inserted into the housing, it's is the pivot for the bellcrank, and also when inserted into a slot and turned prevents the bellcrank from coming out . The T is what prevents the bellcrank from releasing from the housing while the bellcrank is opening and closing the heater door.
The broken T needs to be turned to align it back to the slot to remove it.
My bellcrank was broke at the "shaft" of the T. And that shaft points up and only protrudes from the housing a little. The tool I finally found to remove the broken T was an alligator clip. Like this: https://www.tequipment.net/Mueller-Electric/BU-60X/Alligator-Clips/
the sharp teeth bit into the plastic so I could pick the T up and then rebite it so I had a good hold on it. Then you need to turn the broken T to realign it with the slot while pull light tension upward.
It's a trial and error pick and pull up.
A PITA in a small limited space.
A flashlight and an inspection mirror and you can look down into the area you need to work at.
Put a drop of lithium grease on the bellcrank pivot before installing the new one.
Adjusting the stroke on the cable. You want that heater door the cable moves to be able to close fully in the "heater off" position. Heat on position much, much, less to worry about. In the summer time that door need to be as close to 100% closed for A/C to work well. When you slide the "heat" control to the left COLD, it will not touch the end of the slot, just short.