-
This is what I was going to attempt. I bought new screws and gasket last week, but was worried about attempting this without a spare shower screen.. Might take you up on that if it all goes tits up.
If I was going to use and extractor drill bit I would have to dismantle the machine as the base stops you from getting a tool long than 15-20cm in there (probably why it rounded out in the first pace).
You could still the head off, and then try to remove with pliers once the shower screen is off. I have a spare grouphead block which you can have if the screw gets stuck (plus a spare new screw).
In coffee bean news, Monmouth's Costa Rican Finca Las Lajas is very tasty if you like big naturals (fnar). Lots of fruit flavour.