If you don't want to get the kit you could make a drill guide up. For scratch plate cut ply template as per scratch plate with a steel drill guide over broken screw, drill guide will stop bit wandering. Because of the small size and easy out or screw extractor not available i have in the past shaped a small Allen key to suit. Once the centre is relieved by drilling the shaped key will bite into the hole and you have a handle already on it. The same goes for the tuner screws just a different guide set up. Cost in materials is small. Left handed drill bits also work well in this situation as once drilled so far bit tends to bite and the screw wind out. Any question on a jig I would be happy to help with a drawing or even make one if you want to pay postage(not sure where you are?) let me know if I can help
Cheers and happy new year