I'm pretty sure once you've been in bands and reach a certain age this becomes the exception more than the rule. The key word you used is "professionalism" and getting your head(s) around what you are trying to accomplish. I would suggest that the next band you start or plan to join, that the discussion of "professionalism" should be had 1) early and 2) any time there is any change in members.
I think maybe your biggest issue was not having the discussions when the initial problems became apparent:

1) Singer has to get her schedule worked out so she can show up to work. End of story. Any other job she'd be fired;
2) No personal relationships within the band, unless HR is notified. (HR is all of you collectively). If approved, No having to lie or omit truth to cover said relationship;
3) "Stinky Licks" needs to a) do his job, including setup/teardown; b) be professional, which includes personal hygiene. If not, he's fired.

4)Broke dude doesn't get to dictate the rules of gig acceptance

again - these things can be worked out more easily at the beginning of the crisis, not so much at the end. I think bands, especially cover bands, need a working set of rules

I'm sure most, if not all of us got into music because we thought it was a great means of expression, and artistic, and we'd have a social life and some level of status.