[Oddsock]

Pip used to throw up, whenever she was stressed or had an empty tummy. It was happening several times a week. (She's been checked by the vet)
What's worked for her is leaving dry mix out, in our bedroom, we hear her eating it usually around 3am. She also has access all day, but barely touches it. She gets chicken everyday, otherwise she'd be under weight.
In the morning, and last thing at night she gets- Pet Munchies 100% natural dog treats,duck breast fillets cut into a tiny amount, like three slithers/pieces the size of my finger nail. It seems to stop the sickness. Works when she's excited/anxious also. (Perhaps you could get something similar, if they don't do it in the US)
We thought as she got older, we could cut it out, but no luck so far, if we do, she wakes up, throwing up in the night.
We've tried veg treats, which she gets during the day, but they've not worked as well.

Good luck finding what works for your little one.