How is the tuning stability if you dont use the trem.?
The thing about the 'rocking bridge' when using the trem. is that it doesnt always return
to the 'exact spot' it was in befor you use the trem, which knocks it out of tune. (in my experience)
Go ahead and try wrapping the bridge post with electrical tape, then try using the trem.
I have my bridges taped up, and altho i never use trems, i did try it on my Mustang with the taped up bridge and it seemed to stay in tune pretty well.
And since you already lubed up the saddles, i dont see why this woldnt work.
Good Luck.