Going up Poincianna to 192 and then west there or using Osceola Parkway would be slower than going toward I -4. I got directions on the map and it shows about 40 minutes to MK parking lot. It's very rural out there so there's not many lights till you get to 192.
Did you try Indian Creek, Emerald Island, Oak Island, Rolling Hills, Windsor Hills or Palms? They would be only 7 or 8 minutes from Animal Kingdom. Indian Ridge/Oaks and Sunset Lakes would be 10 min.