That’s not how it works. You have to prove that there is an issue, if you claim that there is. It’s not on everyone to prove a negative.
If someone claims that watching TV for 5min a day will greatly increase your risk of brain cancer, it isn’t on you to prove that it won’t- it’s on them to show and prove that it does. The OP laid out pretty well the issues with current “research” on it already. The reason that there are no legitimate research showing that game meat killed with lead bullets increases BLL when accounting for other factors- is because there isn’t any that show that it is. The only things that have been done is emotional hooks like a picture of a deer from an X-Ray with lead particles purposely put there to show “what could happen”. Or the “grind every single scrap up from every deer- don’t even try to remove projectiles, then let’s X-ray the packaged meat and see if lead exists. Or, shoot deer with fragmenting lead bullets in the chest, then gut them and spray them out (washing the inside chest contents all over the animal) and x-ray the whole carcass and show lead deposits all over the uncleaned, untrimmed, unpacked meat. No doubt those are non-biased actions.