Hum while playing keys is to some degree normal. However, I have seen it very bad. The thing is, I'm not sure what the cure is. Of course always tighten the grounds around the preset panel etc.
I have two installations where we have Hammond's that were perfect in our shop, but have this "hum while playing" problem after they were delivered. In one case we determined it was the location in the building. After years of putting up with the hum, a flood from Hurricane Ike wiped out the organ. (A-100/147a) We replaced the organ and guess what, the hum was now in the replacement! After a few minutes it was explained that they now wanted to organ on the opposite side of the pulpit. Hum went away! So, something related to that location was inducing hum into the organ.
We just replaced a C-3/122 in one of the last church's hit by Ike and they used to have this hum problem as well. The replacement had it to a lesser degree as the pulpit area was completely remodeled placing the organ slightly more toward the congregation. Still, it was there and not present in our shop.
One last story is a church that moved their Hammond C-3/122 into the fellowship hall while the sanctuary was being remodeled. There was an awful buzz which got louder when played. I couldn't find anything wrong but suddenly noticed the recessed lighting looked like those curly florescent light bulbs. I asked if they could turn the lights off and all the noise went away.
So, you may want to check to see if there could be something about the organ's location that allows it to pick up hum that is external.