Let me add this to the mix. The guitar player side fires his amp and leaves his IEM out on that side so he can hear his amp and only uses the other one, for vocals.
I still don't see how the drummer and the bass player can be behind the beat when they're the ones driving the bus. I will add that there's a constant tempo issue because they want to play things way too fast. I think maybe they were playing ahead to speed things up...
That's a great way for your guitarists to damage his hearing, depending on the stage volume of course. Part of the same seminar was about NOT doing that, because the tendency is to turn up the IEM to compensate, which is akin to cranking earbuds to damaging levels. His mileage may vary.
What was the placement of the live mics?
He proposed a couple of solutions. The first was pointing shotgun mics at the audience, sent only to the monitor mixes. Again, this was a pro audio seminar put on by Doug Gould, who's used to working with larger acts. He did mention that for smaller churches (it was a worship-based seminar) that even dynamics help, as long as they're roughly at the same level as the average audience/congregation member's mouth. Look at U2 and Rush's most recent live videos; you can see mics there just for that purpose though Rush used condensors to record audience noise.
For interband communications, he recommended a condensor set up on stage. It helps let some stage volume through, and gives band members a clearer way to communicate. As an alternative, some IEM packs allow for an auxillary input. Band members run a lavalier through this and voila! wireless communication from wherever you're standing, as well as picking up some audience noise and stage ambience.
Please note, I've had limited experience actually putting these techniques into place. I'm just passing along what a wiser, more experienced head told me. We HAVE had good experiences with some of the other techniques he mentioned, like running the drummer's own drums hotter in his IEMs to tame an overly aggressive basher. The key was to slowly ramp it up, if he bursts his eardrums with the first drum hit, he's likely to demand that his own drums be taken down significantly in the mix.