I think Neil is doing a great job on the keys.
This sound thing with the organ, of course is very subjective, but, here's my 2 centavos:
Jazz Organ 3 on the Tyros is really not my favorite if I'm trying for a jazz Hammond sound. I would use another few that to me are much better.
You can also easily mix two or three organ sounds together that can be very impressive.
Also, as far as the Leslie effect, that Jazz Organ 3 preset does have a rather fast and unpleasant sound. But, these settings can be tweaked. If that's the organ sound you want to use, just adjust the tremelo settings.
But again, I don't use Jazz Organ 3 at all, Just MHO, but, yes, Neil has some chops eh?
Scott