I was finally able to render my FC3A silent by removing the unit's base plate and spraying a small amount of DeoxIT Fader F5 (green label) onto the shaft of what I'm assuming is a potentiometer. After just one application, the noise had greatly diminished; after a second application, the pedal operated noise-free. Hope this helps somebody!
The FC-3A may be a refresh or a redesign. It may be an interesting riddle to crack - predicting how long, if ever, the FC-3A will last before making its own acoustic racket. But with the stress you're having to endure from other life arenas - why not bask in the tranquility of your newly silenced foot controller and move on for the time being?
If some form of audible dam does rupture and return you to contemplating the physics of foot pedals - then that can be tackled when/if the bridge presents itself.
Right now you're over sustained untroubled water. Sounds like a win right now.
Just trying to help.
Current Yamaha Synthesizers: Montage Classic 7, Motif XF6, S90XS, MO6, EX5R