Whilst on the subject of drilling into a screw and using Easy-outs:

If you often need to drill holes in just the right spots, a useful
tool is a spring loaded centre punch. You can position it accurately
and then push down on it by hand, till an internal spring releases
with an impact, making a center pock just where you want it. If need
be you can follow up with a heftier centre punch. I wouldn't rush out
to buy one for a single use but it is a handy item for technicians.

There are Easy-outs and there are Easy-outs-Taiwanese style! Whilst
useful for the occasional problem, the Asian made items are of softer
steel and easier to strip. You can generally judge the quality from
the price.

Colin