I watched various live videos of this song, and for one concert David Sancious was definitely playing a Peavey DPM3 ( Peavey DPM3 (SOS May 90) (muzines.co.uk) )
while in another video it was some diffrent kind of synth/workstation (most probably 88 keys with a long row of buttons along the keybed), but i couldn’t see which brand it was…
So anyway, i guess it surely wasn’t a real Hammond but some kind of workstation which was played maybe through a real rotary speaker.
But as David-san stated above: The audience most probably won’t hear a diffrence between the diffrent organ sounds, as long as the playing is cool! 
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Ah, thanks Pianopaul!
Then i’m pretty sure that this large keyboard with the long row of buttons was the Yamaha KX88, which is a Masterkeyboard - so we can not even guess what device exactly was controled with it.
OK, but what is the next point then ? Try to find a DMP3 plugin ? Try to find a DMP3 used unit on Reverb ? From what I understand the DMP3 reproduces some kind of Hammond. Change the FOH engineer and it will sound differently on stage. This is not the central question for playing this song nicely. The audience won’t notice the difference between the sound of hot water and the sound of cold water. And neither will most musicians… If you want to come close from this “sound” the key is to find the closest registration, the closest effects, the closest EQ and the coolest playing.
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