Most of these guys seem to be a variation of the same thing. Similar registrations, method of playing, techniques... I'm not saying that is a bad thing, but that is just one style of many.
Jazz doesn't have limitations, and neither does the Hammond. Back in the day, you had classically and theatre trained organists' mixing with the club scene. I'm talking basslines with both feet, playing the presets, octave and open harmonies, etc. It was much more than an entire album of 888000000 percussion/leslie.
Buddy Cole for starters:
Now for the "living" part of the question... Players like Mark Herman, Donnie Rankin, Cletus Goens to name a few.
There are some very skilled organists up and coming which I've personally heard channeling some of the above stylings, and I have to say I will take these variations over the same-old-same-old.
I'm actually good friends with Mark here, and he never ceases to amaze me with his skill at the Hammond.