I don't have kids Jac, so maybe take this with a grain of salt

I was just thinking, I don't know how expensive those squeezie vegies are, but maybe you could steam some vegies to make "baby mush" as we call it (usually a carrot, pumpkin, spud, brocolli etc steamed and mashed, DH loves it ) like you would feed to a baby you're introducing to solids. Then if you put the baby mush into a piping bag (for icing cakes etc) and either let them squeeze it out themselves or piped it into a face design or a tractor or whatever your child is into, maybe they'd eat more that way?

Good luck!