AI Fingered is cleverer than Yamaha first thought. I'm still probing the possibilities! It does allow you to miss certain notes from a chord, usually the 5th, but as we've seen from the examples above, that's not always the case!
I usually start by writing down the notes that make up a given 'exotic' chord, and its bass note, if different, and playing them with two hands. I then remove the 5th to see what happens, then a different note and so on. Once I've got down to preferably just four notes I start playing with the inversions. Sometimes works, sometimes doesn't, as the notes may be common to two chords.
You'll often have to play in root position, which makes for a bit of jumping around but if you're playing music of a standard that needs these chords, that should be no problem!
And yes, occasionally that * will crop up. It's usually not a problem, as what the keyboard delivers is certainly close enough to suffice, even if it's not 100% musically correct.