I don't feed raw, not that I'm against it, I just don't feel like I'd get it right, but good for you for doing it, I do think it is better for cats.
I just wanted to tell you that my cat Beep is SO allergic to beef, but we did not realize it for years. I feed Wellness canned, and beef and chicken was one of the varieties I would regularly buy, along with chicken and turkey. Well, Beep threw up about 1-3 times a week for years, and we just figured she was a pukey cat. We took her to the vet many times over this, never could figure it out, even suspected a food but since we didn't always feed the beef and chicken, we just somehow (stupidly) never tied her puking to the beef and chicken. I feel so stupid when I explain it now, because it seems so plain, but what can I do now? Anyway, one day, they were out of beef and chicken at the pet store, so I stocked up on chicken and turkey, and then I noticed that Beep had not thrown up in 3 weeks. And I thought, wow, it's the beef! Then a few weeks later, we had a much needed overdue check up with blood work and everything for her, and my vet, (one at this practice) has a holistic approach and is very much into pet nutrition said that he saw beef allergies in cats quite a lot. My cat did not throw up for months after we stopped giving the beef. Then one day, by accident, my husband dropped a big dollop of dog food on the floor while feeding my dog, beef canned food, and she ate it, promptly puked it up within 2 minutes of eating, so that reinforced our belief she was allergic to it. Then a few weeks ago, we were eating chinese food and my daughter gave her a tiny amount of beef from her food, teensy amount, she promptly threw it up.
I just thought I'd pass it along to you, since my cat is HIGHLY allergic to beef and also since my vet said that he saw it a lot in cats. He did say he saw other protein allergies in cats as well, even chicken, but beef he saw far more of. I'd have to wonder if your cat is at least intolerant to the beef if not allergic, since he tolerated the beef heart.
I hope you figure it out soon enough so no more throwing up and he is all good