Is it possible? No it isn’t, not at all.
My daughter, who has the same relationship with food as her dad (i.e. a glutton), couldn’t even stay awake for most of what we ate! My tip would be to drive 15 – 30 minutes out of the park every night and find a little restaurant for dinner, and whilst out visit a supermarket to buy something to make sandwiches for lunch the next day. If you absolutely have to eat in the park then the buffet restaurants offer the best option. If not quality, then at least they offer quality. The Park Side Diner in Disney’s Hotel New York is the best (least worst) of a bad bunch. Pretty much everything we ate (with very few exceptions) was deserving of a TOTAL STINKER award.
This situation is very annoying, given that (generally speaking) the food at Disney parks in the USA is pretty good. It makes no sense to me that the gastronomic French can’t improve the quality of the food here… scarily, the best meal we had all week was at the Buffalo Grill in Calais on the drive home!