I would opt for the taxi, shouldn't cost more than $15-$16 plus tip, no idea what a town car might cost. It's less than 5 miles.
Another option would be to give your luggage to bell services upon checkout from POP, go to a park for the day, and then take bus from park to AKL at the end of the day and your bags will be delivered to your room when you checkin at AKL.
If you need to checkin to AKL first in order to get your park tickets and or Dining plan, then the taxi will probably be your quickest option.