Resort to resort travel is always challenging. There are no direct buses from one resort to another, you need to transfer at a theme park or DTD. You should plan on 60 -90 minutes travel time.
Going to Boma would be easiest on your AKL day. Simply take the AK bus from the park when you are ready. As already stated the challenge will be returning to your resort after dinner.
Another option is to take a cab. I always budget for a cab ride or two for meals, in my planning. It is still way cheaper than renting a car, and basically we enjoy Disney transportation. We find not driving while we are there to be part of the "vacation". It just takes understanding the system, being patient, and planning for a cab or two for the really difficult trips.
Enjoy