Thank you all for your advice and encouragement!!
Here is a picture of the screw. I tried using a rubber band, with no success. Maybe I'm too impatient. My 3/16" screwdriver can't grip it anymore and I fear the more I try, the worse I'll make it. My DH suggests leaving it with the PBblaster for a few days, then trying again.
I found some balance wheels and clutch knob sets on eBay, so at least I'll know where to go if worse comes to worse and I have to drill it off.
This machine was never intended to be a huge project
My fixer-upper is my White Rotary treadle.