Gout attacks tend to be caused by large changes in uric acid levels in the blood which can happen practically with any change in physical activity or diet... I don't know WHY that would happen in WDW
The worst part of the gout attack isn't the attack itself so much as the body's response to it as it attacks the crystal, fails spectacularly and then throws more antibodies at it and that's what causes all the swelling. The trick to getting a "quick" attack is to minimize the body's response.
If your husband isn't already taking NSAIDs or anti-inflammatories regularly (like indomethacin and advil) and its okay for him to have them, have him start taking something like advil regularly the day the trip starts. This will minimize your body's response and keep the swelling down or may cause it to "ignore" the uric acid crystal altogether. (Cherry juice is a natural anti-inflammatory and is believed to work for gout on a similar principle. But I've never had good success with it)
Drink LOTS AND LOTS of water. It's very easy to get dehydrated in the Florida sun and that will up the concentration of uric acid in the blood (which is a change in uric acid levels and that can cause a crystal to form.)
One thing I'm experimenting with right now is megadoses of vitamin C. Atkins (of Atkins diet fame) thought 8000mg/day was a good treatment for gout when people were on his diet (some studies have shown that large doses decrease uric acid in the blood) I don't do quite that much but take 2000mg in chewables once at breakfast and once at dinner and seem to have dodged some attacks. (I am not a doctor, consult your physician/pharmacist for actual advice and drug interactions, blah blah blah...)
One last thing - I "play it safe" on my trips at the beginning and then go hog wild on the last day or two. It usually takes about 24 hours for a gout attack to show up so I figure if I'm going to get one, I'll get it for the plane ride home!
Good luck!