Have you ever played a sax/bass "duet" on piano before? If not, give it a try. Thinking like a sax player with you right hand and a bass player with your left is a great way to get out of any habitual ways of playing jazz piano that may be holding you back.
The key is to think in fresh ways, and really get into the spirit of a specific bass player and a specific saxophonist (or trumpeter, etc.)
For me, this means bassist Ron Carter and sax extraordinaire Wayne Shorter, who played together in the innovative 1960s Miles Davis Quintet. I got the idea for playing like this from listening to their recordings, particularly the studio album Nefertiti, where pianist Herbie Hancock often "lays out" during the horn solos. It's just trumpet or sax playing a solo over a walking bass line with drums too, but no piano (which means no chords).
Without the chordal accompaniment, I began hearing the sax and bass lines as a kind of Bach 2-Part Invention, playing off each other in linear counterpoint. So I thought, "What if I did this on piano?"
Even though I've played lots of walking bass over the years, I hadn't ever tried to emulate a specific bass player's style until I began practicing like this about a year ago. I began studying how Ron Carter was able to play chord changes while disguising them a little. For example, he'd go from Cm7 to F7 like everyone else, but it didn't sound like everyone else. (One way he does this, btw, is by throwing in the 2nd instead of the 3rd, so his line might go C D G Gb F to get from Cm7 to F7. Play it on piano and you'll hear the effect.)
And Wayne Shorter on sax - for me it doesn't get any better than that! I've loved Wayne's playing ever since I saw him perform live with Weather Report and I even got to hang out with him one-on-one in his Blue Note dressing room for about 10 minutes once. We had a real conversation and I was thrilled!
Check out how I play a Ron Carter/Wayne Shorter "duet" on the standard "C'est Si Bon," which you'll find in The Real Book, Vol.1. It's a great tune and it came alive for me in a fresh way when I tried this approach. Emulating Ron Carter led me to play with a slightly different feel than I usually do, and I had fun channelling the spirit of my favorite saxophonist in my right hand lines.
Check it out here, and then try it yourself with a pair of your own favorite musicians. You could do Paul Chambers and Miles Davis!
Learn the 5 Essential Left Hand Techniques with my free ebook: Left Hand Techniques for Jazz Piano
You'll also get my weekly jazz newsletter with practice tips and inspiration