Just got off the Imagination yesterday morning. We docked at the pier on the Navy base on Tuesday. I believe it is referred to as Outer Mole or Truman Waterfront. There was free shuttle transportation to Mallory Square, and you had to meet back at the same area to return to the ship. From what I understand, this is where the Imagination usually docks. If you go to the keywestcity.com there are links to the cruise ship calendars. They show scheduled dates and piers for the cruise ships.
At Cozumel, I don't know what the port is called, but there is a long pier which goes through a duty-free shop and up into the waterfront area with lots of shops and restaurants.
You are right about the limited time in Key West. We ended up taking a trolley tour which went all around Key West. As far as excursions, I would be afraid to book anything longer than a couple of hours unless it was through Carnival. There wouldn't be much room for delay when you factor in time to return to Mallory Square and catch the trolley.
I hope this helps, and I hope you enjoy your cruise as much as we enjoyed ours.