CAUTION - This post contains images that some people may find disturbing
Here is the ugly reality.
Indeed shocking and I understand your frustration, doing a perfectly good job, and then a setback like this. But we never give up. Here my idea to retract the plastic tap

Heat the point to about 400°C press it into the plastic, let cool, pull out the tap, heat again pull off the tap and clean the tool
Location: Mexico city
Printing machine technician
Restored various 1960-70 items
Rock and Roll music
Collecting Vinyl
Restored Jukebox Wurlitzer 1050