Wow, that's a bummer. I'm not an instrument tech by trade, just a
hobbiest/hack. But the things that come to mind are to either drill
it out with a TINY drill (dremel?) or to heat up the joint in the
board (may have to apply a bit of solder to get the heat to conduct
into the board) and try to shove a more intact piece of one of the
remaining pins back through, pushing the broken one out (or use a
mini screwdriver in lieu of one of the pins, they will possibly just
bend).

Either way, you could probably use an extra set of hands. I did with
mine, one of my pins were really in the board and I needed someone
else to pull on the tab while I heated and held the board.

Definitely get other advice than mine, from someone who has
experienced this problem in real life. And good luck man!