Personally I would take a cab. Coronado Springs is reasonably close to the AKL. Taking a bus to the parks other than AK will be back tracking.
Next choice would be to take (in order) AK, DHS, Epcot, MK, DTD.
However, from past stay at the AKL, and having eaten at AKL&AKV restaurants while staying at other resorts, I have some comments about AKL busses. The busses do not shared with other resorts. THis would seem like a good thing (your own dedicated transportation), but there are not as many busses running the AKL route as other resorts. We waited longer for the AKL bus than we did for most other resorts.