Here's a reply I gave in PSRTutorial:

Quoting Al

"On the Organ Flutes screen, you can press the F4 button and the Leslie with transition nicely from slow to fast using the correct transition speed, but you cannot assign it to the Mod wheel. How are you supposed to control this during a live performance from the Main Screen? You must have the organ flutes screen up all the time. Grrrrrrr!!!!!"

Al- I'm not sure what you mean by the F4 button but if you are referring to switching from slow to fast Rotary SP Speed (using the C screen button) the same effects can be achieved by turning the Panel DSP Variation button on (and off) ie. not needing you to always be in the Organ Flutes screen.
As far as "organs" are concerned you can get similar speed up and down effects (through pressing variation) if you set a Rotary DSP on them. If the preset DSP is not a Rotary you'd need to edit the voice in Voice Set, choose which Rotary is closest to what you want and try out the effect of turning Variation on and off. Often Rotary SP5 sounds the "best" to me (as a non organ specialist;) ).
Also note you can edit the variation speed in Voice Set if the fast speed is not exactly what you want.
Although you can't vary it on the fly (eg. via the mod wheel) at least when switched it takes time to speed up, which seems to be one of the goals you were after.

john