We are Atkins eaters and it's not quite the same but daughter eats Paleo and here are the places we had an easier time:
Teppan Edo, ask for no noodles and I didn't have the rice so I'm not sure if you can ask for brown rice but it pretty much leaves you with meat and veggies.
Cape May Cafe had steamed crablegs, peel and eat shrimp, tons of salads etc.
Scrambled eggs are easy at any CS
They have a cart in Liberty Square that has sweet potatoes.
Sunshine Seasons we all did pork chops and green beans
POR has a make your own salad that's pretty easy. You can do shrimp there.
There is grilled salmon and broccoli at CHH
Narcossees was pretty accessible.
We had a lot of salads with chicken but they sometimes have corn or beans so ask and look!
Big hint is ask ask ask...we were on the
DDP and we were able to trade our desserts for water bottles much of time time.
Maybe some of that will help.