I certainly second your endorsement of full-fingered mode. I use it almost exclusively. It requires that you know how to finger chords, of course, but, since it doesn't recognize anything until you press at least three keys simultaneously, you can embellish your playing with your left hand adding individual notes here and there. Play the chord and the accompaniment keeps going on that chord while you could play a chord arpeggio if you want or anything else. In mixed mode, if you hit any single key, the accompaniment immediately moves to that chord. If you are trying to finger chords, but you don't hit them all at the same time, you might have two or three chords sounding before you get the chord you want. If you are going to try fingered mode, forget the Mixed option.
Gary's Gig Disk is filled with styles that happen to be named for a song that they go with. When you load that style, no registration is being loaded. Some of those do have OTS settings and the OTS will be loaded, but no registrations. And I don't think the chord fingering is saved in the OTS. When you set chord fingering, I believe it stays that way until you manually set it to something different. But, however, you stumbled on to that mode, it is lots of fun to play that way. Almost all of the styles available at
http://psrtutorial.com have OTS settings and the left hand is usually turned ON thus adding another instrument to the overall mix -- if you can finger your chords!
Be sure to try working through the "Secrets of Chord Progressions" at that site and, after a couple of months, you will know several hundred chords. I've been working on those chords with my left hand and, if you do the exercises, it does make a difference.