Not what I hoped to hear, but it mostly makes sense...
In Easy mode: E aug because E plus eight half-steps is C, which is an augmented fifth. So in "Easy" mode, this is a two-note shortcut to play any augmented chord. This two-note fingering is not documented in the appendix, although two-note shortcuts for some other chords (such as sus4) are shown.

In "One Finger" mode: This is based on the Yamaha system. When you play any key and a white key to the left, it triggers a seventh chord. So C + E below = C7. Weird, but Yamaha thought this system would be easier for people without knowledge of chord theory, and most of the other brands now have a mode like this too.

Your results in the "Normal" mode surprise me... I would expect "C" with bass inversion turned off. But with "Bass Inversion" turned on, I thought for sure this would give C/E (C with E bass.) In Normal mode I think at least 2 notes are required to trigger a chord.

I sometimes use Expert mode if a song has a crazy mix of straight and slash chords. One thing I don't like about that mode: When you need a chord like Am7/G, 3-note fingering gives you Am7, and it's hard to span the octave to the next G. If you just play G+A it gives the G bass, but doesn't know whether you want A major or minor. I think Yamaha invented this mode too, they call it "AI Fingered."

I agree that 3- and 4-note fingerings are the way to go. But when I try to play music written for organ and bass pedals on a single-manual arranger, the shortcuts really help to reduce the amount of hand movement. Korg's system is pretty good and logical. Personally I like Roland's system the best, but I wish all makes of arrangers permitted more customization in this area.

Thanks for checking these combis!