I know what you're talking about, I had a similar problem. Drilling it out would probably be more hassle than it's worth given the availability of these parts from places like 400fourbits.co.uk or members here.
When pulling my carbs apart, I was fanatical about using the correct screw driver sizes. However with the carbs, I found using a small flat head screw driver gave me a lot better purchase on dodgy screw heads than the phillips heads. So I know it's an obvious suggestion, but go get a small flat head screw driver and try that.