I just plain ol' lied. My mother was the same like yours, probably not as bad but pretty close. She cooks 24 hrs. a day. And like your parents, both of mine also are always munching away on something ALL DAY. It's funny (and sad) because I realized that that is all there is to do but eat eat eat at thier house. I mentioned this to my dad and he said he knows, it's a bad habit, even his out of town uncle said the same thing, he notices him go to the fridge every half hour.
But as far as fasting, I had started to tell my parents, and then they both shunned the idea. My mother kept serving me food on a plate and asking if I wanted to eat and saying "YOU HAVE TO EAT SOMETHING". Eventually, I started making it look like I ate. I would dirty plates, unwrap wrappers, make crumbs, anything to look like I ate and I noticed she didn't ask anymore once she saw little things that I ate. When she asked, I would say "I already ate, I'm okay".
Now, my parents are actually TRYING to fast. My dad one day said he was going to see how long he could go without food. He told my mom to try the same, and they both did. After that, he said he felt alot better than stuffing his face and noticed how much you really don't "need" food, and how their habits have become such a bad one.
Even if you have to break your fast and eat, fine. Just don't say "Look, I'm eating". Rather, make it look like yeah, you ate, so what, not obvious. Then if you ever decide to go back to fasting you can still make it look like you're eating and hopefully she'll believe your subtle clues.
Maybe even your parents will come around, I know mine did. Once they tried it for a few days they noticed it wasn't that bad and they actually felt better not being so stuffed!