Cooked plain pasta (easy for them to do it themselves)
Hummus + things to dip in
Rice - especially sushi type rice so they can pick it up, or even sushi itself
Tuna
Porridge (dd likes the flavoured ones)
Crumbed fish/fish fingers
Oven fries
Smoked salmon
Cold ham
Cold cooked chicken
Dried fruit - apples, pears plus the usual raisins etc
Eggs

Those are all things my DD loves (19 mo) dairy aggravates her reflux too. She does like cheese, but I dont give her much

My other tip is - get some tiny forks, or picks - those plastic colourful ones and let them poke their own bits of finger food. My kids seem to eat way more like this!
Mini muffins or pikelets