Like David, I find the AGS confusing at times. In the electrical bay, at least on our coach model, lives the venerable AGS module. When we first got the coach, I tried programming that module and coordinating with the Magnum remote inside the coach, but it only seemed to result in chaos. The instructions, though concise, were too involved for my limited intellect; even though I eventually thought I understood them, in practice the result was counter to my intent.
As you know, it can be set for a minimum battery voltage, but also timelines, and temperatures to complement the settings on the air conditioners. Any of those could have factored in to crank the genset, but possibly the inverter charger may not have had enough left with all that demand you report, and you reached the low end of the voltage setting, for whatever crazy reason, triggering the genset reaction upon microwave activation.
I pretty much gave up on the AGS, and long ago either set the module in the bay so it wouldn't crank up the genset except in extraordinary circumstances, or shut it down altogether via the remote panel over the entry door. That's not to say I might not yet try to use it to insure battery maintenance while we are temporarily absent one day. Neither does that insure the thing will work as intended
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Joel