Ok thanks to Jezza's prompting, I eliminated one variable when I started to think outside the box. The difference between my gig monitors and studio monitors was because I CRANK output1 which goes to my computer / studio monitors, but output2 going to my gigging monitor was on maybe 40%. When I CRANKED output 2 to 100% the gigging monitors also squeal the same, even when I turn the speaker volume down to almost inaudible levels and walk 10 feet away.
So guitar into Axe-Fx into Alto full range monitor (or Yamaha studio monitor) both produce squealing. Seems like a software bug or something else really weird - because if I turn down the output to 40% and then crank up the actual speaker volume much louder than they were before, there's no squealing. It definitely requires that cranking of output volume (I'm not clipping the outputs though - no red lights come on). Which I can work around if that's all it is, sure. I just would like to know why it happens, and why my other guitar can't trigger it at all.
If I use headphones into of monitor, the squealing happens, but it takes longer to get to full squeal volume (probably because the guitar can't hear it very well).
Also the squealing mostly only happens in full bridge or full neck pickup selection, not any of the other 3 blend modes. Turning off the drive pedal also eliminates the squeal, but my tone definitely sounds worse with that, so I don't want to do that.
Any ideas? Faulty equipment? Known issue?