Done this a coupe of times flush/below the PF surface, its a hack/rough job but it worked out for me, i used a small flat blade screwdriver & pry'd out the wood around the broken screw & i modded up these old Vise grips on the bench grinder & got them out, Filled the core hole with bamboo wood & filled it up the rest with quick wood putty, end result it looked fine & was worth it,