Loose Driver's Side Hand Grip

I need to remove the driver's side hand grip (above and left of the steering wheel) but the bottom Philips head screw was so tight that I managed to round out its head. Can't get a hammer-impact driver in there because the steering wheel is in the way. I'll need to use a screw extractor but I don't know what size to get or what size and type of drill bit to buy to drill the screw before using the extractor.

And there might be another, better/easier way to get that screw out so I thought I'd ask here before I booger things up even more.

 

Update (just for the curious):

Found a Philips screwdriver that was the right size and that fit snugly and relatively straight into the screw head. Proceeded to round out the screw head.

Bought a small screw extractor (the screw is #6 x 20 metric) and the appropriate size cobalt drill. Drilled a hole into the center of the screw and tapped in the extractor. The extractor bit into the drilled hole nicely.

Began to slowly turn the extractor.

Extractor broke slightly below the top of the screw head, so now I'm screwed.

Went inside and poured myself a glass of beer so I would have something to cry in. (And no, that didn't help either...)