Try wax instead of grease. Wax is less likely to pick up gritty debris. Works on squeaky drawers, sliding mirrors, etc.

If you don't mind a bit of a mess to clean up afterward, try dripping melted wax into joints and connections (if the spring is riveted to the supporting shell, etc.). Then peel off the excess.

But padded spring saddles are squeaky. Not much we can do about that. I've learned to just ignore the squeaks on my comfort hybrid's padded spring saddle. If anything the squeaks remind me to pedal smoothly. Often the squeaks occur when I'm bouncing around from uneven pedaling effort. But I keep the saddle on one bike for days when my back and neck are aching too much for the rigid bike.