I know many permies get nervous about genetically engineered foods, but gal-safe pigs were just approved last year for consumption, and are now available to buy for people affected by alpha-gal syndrome.
I think they might have adapted the technology to some poultry products as well based on the website.
Fossil Farms
I am pretty sure you can order a half or whole pig for the freezer.
Maybe this will help if you are open to it.
Edit, further explanation: they are completely 100% pig. No other organism's DNA has been inserted. Alpha-Gal syndrome occurs because the tick's saliva has a substance that causes an allergic reaction. Red meat has a substance (alpha-gal sugar) which is similar to the substance in the saliva so once a body develops an allergy to the saliva, it begins to recognize red meat as an allergen as well. This accounts for the variability in symptoms. People have different levels of allergies, and some people's allergies get worse with every exposure while other people's do not.
These pig's genetic editing was simply to remove the Alpha-Gal gene from their genome. Nothing else about the pigs were changed. Nothing was added to their DNA (like many other GE animals where DNA from other organisms is inserted). They are 100% pig, just minus the allergen. So they are not triggering the allergic reaction.
Hopefully this helps, I just found out about Alpha-Gal syndrome earlier this year, and I can't believe it has been affecting so many people in America right under our nose without us knowing. I am glad a solution has been invented without much trouble, but because of pop culture many people are averse to trying it.