the challenge begins when trying to get things to sound the same in multiple systems
You flat-out can't do that.
You can do your best to make it sound as good as it can on a wide variety of systems. But, there are always going to be outliers. If somebody wired their speakers out of phase or only ran power to the subwoofers or something...there's nothing you can do to make the preset sound right there. Or your song. Or anything else. In a much simpler way, if I like a bright sound, I'm going to buy bright speakers...and your preset will probably sound brighter on my system than on yours. And that's really all there is to it.
The answer, from a modeling perspective, is to get it to sound
good on an average-ish sounding system (not too bright/dark, not too compressed, etc.) at about the volume you want to play at that's broadly similar to the kinds of systems that you usually play on when it matters. It doesn't necessarily have to be perfect, but better is better. Then, you have to accept that there are going to be some variations.
Then, either you adjust EQ and compression/gain/etc. when you get there as fast as you can to bring what you're hearing more in line with what you want....or you run your own monitor mix separate from all that and let the FOH engineer (assuming, of course, there is one) handle the room either by EQing/compressing a stereo mix you provide or by mixing the channels you send them.
You can't control absolutely everything. And if you want to, really the only way to do it is to hire your own FOH engineer. And probably bring your own PA system. And still have the FOH engineer tune it to the room every time you play.
We are in a very interesting time in that it's not that expensive to build your band's rig around a StudioLive or X32 or something like them, hire a mix engineer to build your monitor mixes and one more for a stereo out that the venue can use...and to a great degree all they
should need is a tilt and a couple shelves, maybe a safety limiter, and tune your already well-mixed stereo output to their system. And if you do run your own sound, you can do it the same way, it would just be one of you walking around for a bit with an iPad to set those few controls that really matter. And as you do it more, you should get pretty quick at it.
Why more small-ish bands don't do this is completely beyond me.
Short of that, embracing the variance really is the only way forward from that problem.