Turns out I had overlooked that Mute button. I’d gotten so used to the other way of thinking, where On/Off means On or Off, not mix assign.
I put very little in the monitors. Whenever a mic is not in use, I don’t want it adding to the stage. So downstage solo mics, for instance, whenever there is not a soloist standing in front of it, I turn it off. Typically the only thing in my front wedges is vocal mics and solo mics. Occasionally if it’s a difficult venue the band will request a little piano or guitar so they can keep a pitch reference and sometimes a little overhead for timing reference. I don’t think I’m mixing monitors wrong, thanks 
My philosophy on mixing live sound for big bands is for the audience to not even know I’m there, and to think that everything they’re hearing is just coming acoustically off the stage.
I forgot to mention in my original post that due to space constraints at most of our venues, I seldom have a FOH position. In fact, when we purchased the iLive system a few weeks ago, we didn’t even get a control surface to go with it based on our positive experience controlling other digital consoles remotely via iPad. I am finding that I need to also have the editor up due to limitations in the A&H app, so now I’m going to have to insist on finding a table and creating a mini-FOH.
