By the way, we've been in this house for 2 1/2 years (new construction) and it's just now started to trip. No changes to the dishwasher or outlets have been made since we've been there...

I am taking for granted that the dishwasher is on a separate circuit from the island gfi, at least it should be. My first thought is that the wiring going to the receptacle on the island by the dishwasher was installed with the cable running past the diswasher and each time the door was opened there was some movement of the dishwasher against this cable until it was damaged and now trips the gfi. Take the bottom plate off the dishwasher and see if you can see the cable going to the island receptacle. Then check it for damage where it may be touching the dishwasher. Hope this helps.

Ron

there is a switch for the door to stop your dishwasher if you try to open it- could there be a problem with the wires to it or the switch is grounding out???? that would be my guess.

If the four duplex recepticles (first one being GFCI, and the three that follow) were "cheated" then the movement of the door, as the diswasher is strapped to the counter above, and prolly has a backsplash glued to the wall, could be transmitting enuf movement to cause the GFCI to trip. GFCI recepticles are only allowed to be "back stabbed" meaning the wires are stabbed into the back of the outlet instead of screwed onto the correct side screws, if they are solitary or end-of-run. If they are providing GFCI protection to the remaining three recepticles, it should be post wired (on the screws). That could be the problem. (UL references that are cited in NEC), none of those recepticles should be back-stabbed.