We didn't want to move the drain, so we focused on putting the island where the sink could reach the existing drain. We also wanted to keep the junction boxes where they were mounted, and mount them inside one of the cabinets. It was a little tricky carving out the base of the cabinet to fit the drain and electrical conduits, but we managed to arrange the island to get it all fitted nicely. We arranged the cabinets to gauge spacing before we actually started digging.
We had to turn the cut off valves around so they would be accessible, remove the vent pipe, and run the water lines in the ground, so dug a trench in the concrete slab that ran over to the nearest exterior wall, where we ran water and vent vertically to the roof.
Up on the roof, we had to redivert the water lines to run down the wall to connect to the waterlines we ran from the trench, so we tapped into the existing lines on the roof. After the new copper was installed, we covered up the pipes with more insulation and spray foam.
We filled up the trench with gravel, sand, and concrete. The island loop was necessary to ensure the water drained well, and backflow exited to the vent instead of backing up into the sink.
We then installed the cabinates onto 2x4's, and secured the cabinets to each other.
We installed the dishwasher to make sure we had the right cabinet height and ensure our countertop would mount nicely.
We installed an undermount sink, disposal, and insta-hot water unit, and used a router to get the sink edge flush with the plywood sub-counter. I installed the faucet, temporarily, so we could get a working kitchen back in order, while we spent the next couple months on the concrete counters.
Sink: Miseno 32" from Build.com for about $350.