I can tell you on a trip earlier this year in Aug (two day before hurricane Charley hit) we had to walk in the worst rain storm I had ever seen (up till two days later anyway). We walked from Cirque to make our dinnner reservations at Rainforest Cafe.
If Im not mistaken that is from one end to the other, and with the rain (which may have sped us up a fair bit) it was no more than a 15 minute walk.