There's no excuse in all the world for "euthanasia" to take more than a few minutes TOPS. Over weeks? That's a horrific concept.

Please do not go through with that. I would feel very uncomfortable with a vet making that suggestion.
Most emergency vets, even if they are not 'all animal' vets, will euthanize an 'exotic' or farm animal with injectable drugs, usually sedatives, and it's over in moments. Otherwise, I STRONGLY suggest something like CD or a simple cutting off the head. You can place the body in a cardboard box with a shroud for burial. Even slitting it's throat and bleeding it out would be more humane than days or weeks of suffering.
Also, DO NOT try to gas this bird. CO2 is only appropriate for very small animals weighing a few lbs. Your turkey, and indeed most adult chickens, does NOT qualify! Additionally birds have exceptionally sensitive respiratory systems. CO2 poisoning/gas will be VERY painful for it.
As a whole veterinarians agree that cervical dislocation, in all it's forms, is the most humane method for home euthanasia for adult chickens and many other animals. I can't imagine this being any different for adult turkeys.
Perhaps if you can't find someone to follow through for you, you can reach out to other local poultry keepers and ask them to do it for you. That way if the head is removed you never have to see it before it goes respectfully into it's box.
Additionally, if you find a vet to do the injectable route, please make sure the remains are buried deeply with a stone on top. Gravestones first existed so that wild animals would not dig up the bodies. You do not want a wild animal to dig up the drug laden turkey carcass and eat it.
I'm very sorry for your loss. I hope you think deeply on what's best for the bird and causes the least harm.