Those symptoms can also be related to bugs, particularly H. Pylori. If a small dose of betaine gave you problems then you might not have hypochlorhydria.
Or it could be just really complex. Gall bladder blockage can exert upward pressure and prevent the stomach from releasing in proper time.
Very rare meat requires not much stomach acid to digest. Well, actually it needs to be raw, something like carpaccio.
You could also try raw eggs/yolks.
Low adrenal function can be a cause of hypochlorhydria. You can slowly rebuild stomach acid with salt, lemons, ginger, beets, apple cider vinegar.
Also you can try different cooking methods. I would think the opposite spectrums will be worth a go, rare meat and also meat that is stewed /cooked for a very long time until it almost falls part. Gelatin technically is a protein and I would think it's much more hypoallergenic than muscle protein.
What exactly are the symptoms you experience from these food allergies ?
You could try protease enzymes, lipase, pancreatin. People with low stomach acid usually experience a feeling of food just sitting in the stomach and not releasing. With meat they feel very heavy.
Stomach acid sets off a chain reaction of digestive hormones, in particular it is one of the triggers for the gall bladder to contract.