Eazypower Isomax-One Way Screw Removers.
Grainger Item #:
42W495One Way Screw Remover,No.6 to No.14,PK 6
I have used this before for painted and unpainted screws. Some screws come out easier than others.
I was able to reuse the screws after i took them out and replaced my hardware.
If you know the size these are also available in single packs.
The trick is setting the depth of the center bit and applying pressure directly in as the outside and center of the tool grab the head of the screw and remove it.
I had a learning curve the first time i used this but I use them all the time and love this product. I have also used it to remove damaged bolts.