I might try offering a small amount of food every few hours throughout the day. Maybe Brodie's tummy would tolerate that better than just offering couple times a day.

When humans have tummy troubles plain white rice stays down. I'd make some up and try it. Worse that could happen, he throws it up.

Only other thought is since he is throwing up so much withhold food for 24 hrs let his tummy settle down, leave out plenty of water for him to drink.

I'd check with the vet again see if you cant give him something (medication) before he eats. It's available for humans, animals should be no different