Don't forget you can add lentils (especially red ones) to thicken up a sauce, sprinkle nuts and seeds on yogurt and peanut butter are also ideas that have worked for me as is hummus which is sesame and chickpeas so has your essential fats and protein.
(I have only been a veggie two and a bit years and have run marathons as meat eater and veggie and found no real difference to my ability).
I found just throwing in a bit of speed work made a difference.
So once a week, on say a 4 mile run....
Running my "normal pace" for a mile and then spending two miles running faster between say four lamp-posts then going back to "normal" again before speeding up over another random distance be it two roundabouts or to the next litter bin before spending a mile back at my "normal" to finish.
I have non-running friends who last October were puffing after half a mile. They then got to a point they were grumbling at running "12 miles this weekend" and by the end of it they were cheerily saying "ONLY 12 miles this weekend" They got around London in just under five and a half hours.
Totally agree speak to your GP, preferably your neurologist as NEADs and epilepsy can be so, so different from one person to the next. I can only really comment on the seizure side as I believe the causes for NEADs can be different from that of epilepsy although the outcomes are the same.
Is there a pattern to your seizures? Do you know what causes them? Are you suffering from full-on tonic-clonic seizures or "funny turns" (excuse the term funny turns but they can be so varied from staring into space to walking around in circles mumbling I can't think of another word.)
There are a few devices out there that can sense and send an alarm to a friend/relative if they sense you are having a fit (I think they are based on if they think you have fallen over).
If you decide to run always let somebody know where you are going and how long you expect to be. I usually have a piece of ID on me should I end up in a hedge or something.