I think all of your problems could be solved by a car rental, but I guess not an option? Also, it appears you would really rather do Universal than WDW? I took a cab from Universal to the airport once, if i recall correctly it was around $40-50.
I don't know how the Double Tree rates. I do know that your day would be well spent just lounging on the beach or by the pool. Since you aren't driving, a trip to Cape Canaveral Space Center would be very expensive considering admission and taxis.
The port is about six miles from the Double Tree. Not sure how much a taxi to the port would cost. You should ask the Double Tree if they have a shuttle.
Also, how many in your party going to Cocoa Beach from Universal? Are you sure you don't want to drive? These transfers are adding up for you.
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