HELP- Broken tuner peg
Instruments- discuss specific features, luthiers, instrument problems & questions
It looks to me that the string hole is now more-or-less a slot. First, I'd try using a screw driver, but not really expecting that to work.
My second try would be to deepen the slot with a saw and files. This would require removing other strings and maybe some pins. I think that would require less skill than drilling for a screw extractor.
It also looks to me like the string hole in the broken pin might have been off-center. I would also be concerned about the variation between notes in the string windings.
If the pin holes do not go all the way through the wood, some may have bottomed out. The pins may not have been backed out enough before winding on the new strings.

(...and what a nice t-shirt you are wearing, Robin
. Just call me an agitator
(or maybe a gremlin).