I usually drill till i feel screw, and screwdriver and small hammer for end to clean. If you got hexagon, torx type screws then switch to smaller drill and drill inside hexagon also and use something small to clean the rest. After change screws. Done many times.
I offer client to choose with or without. If they choose with then i warn then they could be off center but if they want in center also no problem just order extra cloth an pay more. One client has ordered extra cloth for that. If you want logos not streched out, start with logos and then corners.