Get good at freezing things
My daughter has trouble with deli meats. Fortunately a grocery store we shop at carries organic packaged deli meat. This means no nitrates or other preservatives. My daughter does not have a problem with this meat, which is great as it gives us something else she can enjoy.
The problem is cost. This stuff is not cheap and does not keep very long. Toddlers don’t have big stomachs either, so my suggestion is to freeze some after you open it. This should help to save you some money.
