The 1/2 cup of food thing-- that's not how most people with the band eat, as far as I can tell. It's a number that gets thrown around a lot-- but it's because that is 4oz by volume and I'd say most people eat 4 oz by weight (which is not half a cup).
So 4 oz of chicken isn't whatever you can mash up to fit into a half-cup measuring cup. It's 4 oz by weight of chicken.
I probably eat up to a cup (in volume) of food most meals and I've been losing above the expected weight per month.
Edited to add: Your doctor is going to give you a "one size fits all, most restrictive possible" program to follow. But the fact is, you're going to have to figure out what you can do that's safe but also that allows you to lose weight but live your life.
This is completely opinion-- but I think that people who have the most struggle with the band are people who have been told they shouldn't be able to eat more than 1/2 cup of food, 3x a day, and that amount should make them full. Because those are the bandsters who search for such tight restriction to force that 1/2 cup issue that they are way way too tight and develop problems like acid reflux and an inability to eat healthy solid foods.