Fascinating thread and surprised that I didn't see it back in the day.
Specifically to answer Prince of the Halfling's fine post:
Sauron could easily have swayed the Eastern and Southern men to fight for him without lying. Military glory, security from Mordor, crusade against the Western and Northern men; lies were not necessary.
Likewise the Mouth. Why assume that Sauron lied? Mouth could easily foresee that Sauron would need to delegate some fun jobs!
I have to agree that Sauron did all his best lying further back in the story, and that's why I'd choose someone else.