After much discussion with the homeowner, we decided to make the island smaller by cutting off one of its corners.
We experimented with the shape of the new island, putting masking tape across the counter so the home owner could visualize the results and we could be sure there was enough depth to reinstall the microwave.
With the top out of the way, we found that the lower portion of the island consisted of two standard base cabinets in an L shape with 2x4 stretchers spanning the unused space behind.
On removing the smaller cabinet, we were surprised to find waste and supply lines coming up through the floor where tile should have been.
Evidently, the previous island had contained a sink. Unfortunately, this area of the floor would be in plain view after we reconfigured the cabinets, so we were going to have to remove the pipes and replace a couple of tiles.
We repaired the mud bed with quick-setting cement, and used leftover tile to patch in the missing section.
With the countertop in place, the reworked island looks original, but the kitchen bottleneck is gone.