FWIW...
Last spring I decided to "upgrade" to a set of Sidi Genius shoes. Within 30 days, the notorious
squeak started.
Tried Johnson's and ArmorAll, seemed to be a temp fix. Soon as the lubricant wore/washed off, the
squeak returned.
Tried a 1" square of rubber between the adapter plate and the shoe. Seemed to work except on hills
(especially 8% or better).
Figured that if a small rubber square worked under most conditions, then bigger *must* better.
Had some spare automotive-type gasket material in the garage. Removed adapter plate, traced outline
of adapter plate onto gasket material, trimmed to fit, cut holes for cleats, then placed the "shoe
gasket" between the shoe and the adapter plate.
Took 'em for a spin yesterday.... several 8% (and better) climbs and nary a squeak.
Your mileage may vary.