Hi there!
My husband has epilepsy and let me start off with the good news- everyone is different but many epileptics do Disney with NO problems whatsoever.
Papa Who's biggest challenge is remembering to take his meds when his normal routine is thrown off by vacation. Enlist your parents to help, get a daily pill box, set alarms, do whatever but make sure you stay on your meds!
The best way to reduce time in lines is FastPass. Yes, there's a Guest Assistance Card (GAC) which helps some people but it won't really keep you out of the heat and it won't shorten your wait times like FP does.
The coolest part of the day is early morning until about 10:30 or 11 am and again in early evening. So, many people try to get to the parks early at opening, leave midday when it gets hotter and more crowded and thn come back in the evening.
Animal Kingdom feels hotter to many people (and also more humid). We watch the weather reports and try to go there on one of the cooler days during our stay.
Know where the first aid stations are. They are air conditioned and relatively quiet and if you start over heating they are a good place to rehydrate and relax.
Do you have other triggers?
Guest Services can let you know where you might run into things like strobe lights. (They're not an issue for Papa Who, but I know they're a common trigger.)