Whoa, quite a thread. So nobody's covered Shai so far? How about Boyz II Men, at least? They had quite a few hits and people still remember them today, but the harmonies make it very very difficult.
The only 80s new wave I've covered live was probably "Mad World", but I'll play a lot of stuff like "I Ran" or "Call Me" when I DJ, especially after 3 AM or so. I could see a band that does nothing but that and has hair and everything doing quite well.
Boys II Men? Shai? Can your band pull of perfect 3-4 part harmonies, along with multiple synth parts? Exactly....most cover bands can't.