I realize that bass lines use the root and the fifth quite a bit. So all of sudden, without having played very much bass, I start hearing those lines with a bit more clarity, just by intending to play it. And, what should have been obvious: the piano doesn't have to play the root and the fifth very much, because the bass has that part covered, so the piano concentrates on the third and the seventh.
A voice in my head says: your songs rely on easy harmonic and rhythmic tricks, and they all sound similar to one another. I answer this voice by saying, well, I am a hobbyist, but honestly I don't feel my songs are inferior to those of anyone, except Cole Porter, Harold Arlen, George Gershwin, Duke Ellington, Richard Rodgers, and about three dozen other songwriters.