Some tuners do not have retaining nuts as described by Graham but have instead , metal bushings that are pressed into the headstock. I do not know what the F-180 has but my only Yammy, a 1980's FG-512 uses this type. In these the little screws do hold the tuning machine in place and the bushing holds the shaft true. I also have an old Framus in which the bushings had fallen out and were lost. The shafts then wore the wood away so that they were no longer true. My solution was to drill out the holes to a slightly larger size and then insert a brass bushing with an inside diameter to fit the shaft.It worked like a charm.
                      Sandy
P.S. I would fill stripped screw holes with wood and glue over a wood filler. A round toothpick works great.