Plan on 11-5.

Seriously. It starts to get murderously hot around 11 (the humidity is what makes it so miserable) and won't really ease up until much later, sometimes not at all until the sun goes down.
For fast weight loss that is safe, check out MediFast. You can drop 30 pounds safely and quickly, if you follow the plan. Exercising is fine, but without a decrease in calories, it really won't help much. (One of the great misunderstood aspects of all time). I won't natter on (can you tell I'm a crusader?

) because I know how boring that can get, but seriously if you want to drop fast pounds, it's a viable method.
Be sure to bring only natural fiber clothing. Anything with the twins is going to make you feel like you are wearing saran wrap.
Be sure to have those good shoes.

Either the Keens that you've mentioned or others that are very comfortable. You'll want to be sure your socks (if you wear them) are thick and comfortable too. (Not to mention those "unmentionables"

yep, they need to be light, and cottony too).
Be sure to have a lightweight hat. Something that the air can flow through, but that the sun will not beat down directly on your head.
Sunscreen is a real issue for me. Most of them make me miserably hot, and sticky so I now only use Neutrogena. I used to use only Bain de Soleil but I can't find it anymore.
Drink buckets of water. Seriously. You'll be amazed at how much you'll need to keep yourself from feeling nauseated.
Oh, and be sure those light comfy clothes in natural fiber are all light colored as well. Loose fitting too.
Bring mosquito repellent with DEET. It's nasty stuff, but so are those 'skeetos. They'll eat you alive if you let them. I use the spray on my clothing, hat, shoes, ect. and try to keep it off my skin as much as possible.
Sunglasses, too. I'm always amazed at how many folks show up at WDW in the dead of summer and don't have sunglasses. Talk about headache!
Hope that helps some. I've had some serious run ins with the heat at WDW, so now respect it mightily.