Why not thin some GREASE with a volatile solvent (acetone, for example) to make a liquid? Flow it in and let the solvent evaporate, leaving grease in the bearings. I would think pumping the pedal full of grease until it comes out the ends would make a greasy mess as the gross excess of grease migrates out for the remaining life of the pedal. Moderation is the key to using grease on a bearing. JMHO.