[Limey_Dave]

I suspect you may have started with too large a bit,with a 1/4" derby cover screw you only need around 3mm,this would have hopefuly left enough slot to pop the heads off and leave some "trunk" to remove the screw.
The screws are Grade 8 so quite hard to start with but a Dormer,Osbourne,etc drill idealy tin coated and ground flute.
The Makita although HSS was prob a Jobber Drill that are disposable and not the best for accurate work.
If you use 3mm you need min speed of 1100 RPM but main thing is to keep it cutting not rubbing.