"When the Clowns come Home" - Widespread Panic
"Desert High" - Billy F. Gibbons
And then, when those were shot down, and I saw the oldies trend,
"In the Summertime" - Mungo Jerry
I could imagine Mungo Jerry would go over. The other two are songs that are recent but sound like they're old, and no one would know them. Sad reality of the cover band scene - the crowd is not interested in getting introduced to music they don't already know. If you're getting gigs to entertain a crowd, you've got to meet them where they are. That's not saying your band ISN'T lazy and using the play-what's-familiar mantra to excuse their laziness, but I wouldn't expect those other tunes to work for any band (other than the original artists when they play for a crowd of their own fans).
I like to allow for each band member to get one "vanity" pick, whatever obscure tune or deep cut they want to play just because they want to play them, precisely for morale reasons so they don't wind up feeling... like you're feeling. But no more than one.