Was the acid reflux as well as high metabolism something that was diagnosed by a doctor or is this the mother making a diagnosis?

Because that seems like a ridiculous amount of food. I would not be ok with having to serve food at random times of the day, here we eat at set times so it would have to be a valid medical condition for me to make an exception. And I also agree that when you have acid reflux, eating definitely makes it worse at least in my experience.

Should he not be on meds if it's that bad?

You for sure need to raise your rates, or ask the mom to start pacing a lunch or both at this point because it is a lot of trouble for you to feed him at hock.