You still have that sax? I play the piano like a guitarist. Both my hands do essentially a similar thing. It's very difficult for me to get them to act independently. We have a piano and I play it often but really just chords, nothing elaborate. It's a nice piano though and I love its sound.
We sold the sax after school, unfortunately. Did you learn to play piano traditionally? (I'm not actually sure it there is a non-traditional way to learn, but I imagine there is). I imagine when I learn piano I'll play like a guitarist. My plan of attack, if I ever do get a keyboard of some sort to practice on, is scales scales scales. One of the first things my guitar teacher would do - after requisite basic music theory - would be to get the student(s) in the jam/teaching session to play the basic background track to a song and then just shred on top of it. Afterwards he would show how, using basic scales, he learned to solo like that. I was blown away at how a simple pentatonic scale could sounds so amazing when fiddled with over a simple three chord progression. Needless to say, he rarely had a problem with students not practicing at home. I don't know if the same logic applies to playing the piano, but I figure it's worth a try.