I've gotten the "grazing" comments... time for a feeding... even a couple of jokes about how it might be easier to strap a feed bag on my face. Haha. (Hey, might be onto something there... just kidding!)
I think in those instances where it would be inappropriate to eat, the best thing to do is not eat. I would definitely not eat in church. What I *would* consider doing is packing a few crackers or something of the sort to quickly snack down on before the lunch afterwards. It's not a calorie thing, but rather, if you go that long without eating, sometimes your stomach can be a little touchy if you immediately put a big meal into it.
Now that I see your work situation, it might be a more practical idea to *slowly* increase the amount you eat at your "feedings". By "slowly" I mean taking maybe 2 of those mini-meals and adding 100 calories apiece to each of them. Give that a few days, then do it again with another 2. 100 calories isn't much - you're talking a slice of bread with a thin scrape of jam or margarine, a serving of dry cereal, a banana, 2 graham crackers - so it shouldn't be enough extra to make you feel ill. Your body will get used to the additional food pretty quickly.
I really want to emphasize that you're doing it right, by the way. Small amounts often is definitely the way to go!