If I understand correctly, you're getting water leaking out of the kitchen slide itself (underneath/outside) and that you've determined the leak is probably in the icemaker water line (frost-colored plastic line that runs out to the slide along with the gas and electric lines)?
If that is the case and you are turning off a cutoff valve somewhere behind the UDC and it is still occurring, I suspect the cutoff you are turning off is not the icemaker cutoff. We have a 3690 and went through this same exercise before I happened upon our cutoff.
The cutoff valve for the icemaker water line on our unit is in the cold water line running to the sink under the counter in the back. Trace the blue water line from your kitchen sink faucet towards wherever it comes up from the floor and you may strike gold. Can't guarantee it since they re-routed the plumbing in the newer units with the molded rear cap (ours is the older, flat back unit).
By the way, after water leaks from our icemaker water line on three different occasions in three different locations, we gave up and now just buy ice by the bag.