To remove the broken grubscrew, try using a "left handed drill " There are such things! With a bit of luck it will bite in and start to unscrew the grubscew.
The thread is probably BA. At a wild guess, 2 or 4 BA.
DON'T be tempted to try using an Easyout. TOTALLY misnamed.
If the worst came to the worst, if the remains can be got out, but the thread is damaged, it could be restored by drill and tapping oversize and fitting a bush, tapped to original size.
This might entail some reassembly, machining and hen stripping down again.
The surface should clean up with careful use of emery on a file. Any slight removal of metal will be compensated for when setting the tool height.
HTH
Howard