What a bluff Paul, very sorry...im looking for one solution on spanish luthier forums and find some possible fixings, all of them requires lately refilling with some piece of wood, like a toothpick or something.

The ones i've seen are:
1. Do nothing, if not the lower springs of the machine head, just glue them with some metal superglue for aesthetics purpose..(just the easy one)
2. If you have a drill press, try to make a tiny hole (or maybe 2 around with the same diameter) near of the screw, and maybe you could extract them with some pliers.
3. get some of this tools (here named "sacabocados") and using the smallest try to carve a hole around the screws, not necessarily entire length of the screw, just enough to get the tip with the pliers and extract them.

http://www.ebay.com/itm/9x-Sacabocad...wAAOSwDN1URcp4