Well, sorry to have discouraged you! Like others, I've been confounded with how to work with the volunteer & non-professional sound folks in this situation. Another way to look at this is that it's also hard for them, because they can't know what it's *supposed* to sound like, since there's nothing for them to audibly hear when you are playing. For all they know, it's supposed to sound like fizz, or whatever. And, likely they are not listening to the monitor mix when it's going back through a submix, i.e., you don't have a dedicated person working the stage monitor mix So, ultimately, even with a mic'd amp, the sound in the house may not be what you are hearing. But, in that situation, both you and the sound folks have something to listen to be compare the house against. So, if you can use an amp, all of this (POD HD direct) gets a lot easier if you have the ability to use a small power amp on stage as a monitor, and split the signal that you're sending there. For me, the problems have all been due to the mismatch between how I expect it to sound, and what I actually hear in the IEMs once they're screwed in, because there's nothing else for me to listen to.
With all that, we have Avioms, and with my constant whining, I've managed to get the house sound fairly consistent, but the monitor mix still can be random, due to changing folks behind the desk. Even with the ability to recall scenes on the Yamaha mixer, I can't rely on them using them, so the gain on my channel (which might have been used for something else in a different service, or maybe everything was reset due to a t-storm power cycle/surge) is subject to change. So, I've actually switched to using a digital recorder/mixer to monitor myself. I take my Aviom feed, and remove myself from that mix, then take the L/MONO out for the house and my digital recorder. Almost the best of both worlds, save the 2 extra minutes of setup time to run 2 more cables and set recorder levels. But, at least now I know that what I hear in my ears is exactly what's going to the board.