I'm looking for some suggestions about how I can stink a little bit less on piano. In my role, I use the piano with some frequency, and I'm skilled in reading music and playing melodies or chords, but not both (outside of the basic I, IV. V, maybe vi), and forget about anything with parts. I'd really love to be able to play accompaniment to simple songs outside the basic boom chick boom chick left hand right hand pattern. For example, I'd like to know a few different ways to play along with Twinkle Twinkle Little Star so I don't fall asleep at the keys. I've tried using method books to improve my skill, but they're either way too hard or way too easy.

Can anyone recommend any exercises, etudes, or anything else that can help me seem like a better piano player than I am?