You could make your own--much easier to control your spices/salt that way. Make a batch, freeze them on a cookie sheet to keep them separate and then bag them up. []
If you want healthy, that's the way to go. If you want budget, not so much! Where I live two chicken breasts cost $10.
You can buy the bargain breasts, but they are thin and full of added fluids, chemicals, and preservatives. (The ones that come in bags of 8 or 10.)
OK--Minor hijack here--sorry--That surprises me. I am able to buy good quality fr/org chicken breasts from a local butcher for less than that. It isn't quite as inexpensive as the big freezer bags or fresh on sale, but it's far less than the price you pay. Places like Whole Paycheck are pricey. I wonder if you might find better prices if you shop around.
The other part that puzzles me is the implication that you would feed kids the premade nuggets because they're budget, but wouldn't feed them homemade nuggets made from the frozen breasts because the breasts are filled with additives. I find that to be a curious jump in logic, but perhaps that isn't what you're saying. To me it seems like a great middle step in moving toward a less processed diet without upending the whole applecart.
Anyways---OP--I hope you find a brand that works for you. I remember my nephew crying because he got a bite of pickle on his burger and it was too spicy (poor kid). Seems funny at the time, but when you have a supertaster there are all kinds of little things to deal with that you never expect.