It was easy to get my attention with this one because Latin jazz is my favorite type of jazz.
I love it overall; in particular, the unique percussive intro, and it's segueway into everything else. I think you really succeeded in selling me on the "live" feel with that. Other strong points in my opinion are the piano like you said, and even the guitar thus far.
I can't help but think that the horns need something, though.. What, I'm not sure, but they give away "synth", if you're trying to avoid that.
Overall, really digging this; I'd love to see where it goes.