Joe, I think I'm between you and Mac - I learned piano via Fingerpower, some Czerny, some Schaum, and hard-core learning of classical pieces that took me forever.
Then my teacher caught me noodling out some Journey tunes from the early 80's and asked why I was playing those.
That started me down the road of chord theory.
In 1985 I started self-teaching guitar and played pretty much open chords.
In late 80's I had learned pretty much how to comp on piano with gospel/praise music chord charts. One very crucial learning for me on this was chord inversions. Even the simplest major, minor, dominant 7, major 7 and minor 7 chords are a good place to start.
Learn 'all three' for each of them. Just like you can make chords across the fretboard for most I IV V songs using 'simple' chords, you can do the same on piano/keyboards. BUT, you need to know the inversions. You can probably play the 1 3 5 version of most chords. Get your hand used to the 3 5 1, and the 5 1 3. (these being the triad components or whatever the right terminology). Take note of how to jump from the 3 5 1 of the I chord to the 1 3 5 of the VI chord. Get your hand used to that. Interplay all of these and pretty soon you'll have your hand practicing the 'path of least resistance' between the various common chords and inversions. These are all pretty simple for me now, including add2 sus4 chords. Now I'm starting to learn some jazzier chords as well, but it's taking time.
I have been able to translate some of this over to guitar, by getting my mind out of Barre chord mode and using simple 3-note chords in several different positions and moving between these inversions with minimum fretting hand movement. I STILL need to really learn my fretboard, after playing all these years. I have the bottom 4 strings and the top e string (from playing bass these past few years - you have to know the fretboard), but that pesky b string still is somewhat of a mystery!
Also look up Scott the Piano Guy Houston on PBS and on-line. His method, would pair nicely with your goals. I kind of self taught myself some of what he teaches.
-Scott