I use these left hand bits from drillhog to extract screws when they get stripped.  If you want a set, got them on eBay from here: https://www.ebay.com/usr/drillhog 

This is a quick box I made for my left-hand drill bit set of 13 imperial bits from them.  Adapted via openSCAD model found here https://www.thingiverse.com/thing:4405296.

Modified openSCAD file included so you can customize too.