Kevin,
Starve or suffer are not the only options. You have very serious medical needs. Given all the crazy diets people follow there is no need to apologize for not eating what you cannot and should not.
I hope the following ideas are helpful, they can be adapted to any dietary needs. I have kept kosher for many years and have been in situations where I either could not eat the food available or was where there would be no eating facilities such as long doctor appointments at inconveniant hours, out running errands or traveling. Because I have hypoglycemia and also get dehydrated very easily I always try to have something to eat and drink available or find a place where I can get something to hold me over.
Use "portable" food. Much food now comes in pull-tab cans or sealed packets. Pick up or buy indivdual packets of condiments and salad dressings. Canned sardines are an excellent and nutritional food. Applesauce, peanut butter, salads, fruits and veggies are available in individual packs and do not need refrigeration. Bananas are wonderful. Chips, crackers, candy and such can help kill hunger and not all are bad nutritionally. Small individual box drinks, juices, long shelf life milk, soy, rice and almond drinks are very filling and can be consumed quickly. And of course there are sport drinks and nutritional supplements. Also "health smoothies" I love carot juice!
If you will be out for a while there are many sizes of soft insulated containers to carry cold food and drink. I always travel with a small immersion heater, coffee, tea sweetener, plastic utensils a cup,etc. Oatmeal and grits come in individual packs and make a filling breakfast. If you will be traveling or out for a day or longer frozen food can be taken and either heated in a microwave or allowed to defrost. Also if you are staying over somewhere use the ice bucket in your room to keepthings cold. Most places can provide more than one.
There is no rule that says you have to eat when others do. If I know that I will not be able to eat a regular meal at a reasonable time I eat a filling meal earlier, take something light until can eat or rely on snacking.
Take advantage of these meetings to educate others about OC. You never know when your words could save someone's life.