I am having the same issue my heart is breaking I have to put my turkey down to she is the sweetest animal I've owned but she's truly suffering her feet hurt her just thinking about doing it kills me but I'm being selfish by keeping her like thatThis is never an easy decision to make nor even discuss. I'm sorry your having to go through this.
I've faced it numerous times with young Poults and Quail Chicks but not an adult Turkey. The method I use on smaller ones may work if you have a big enough box he would fit in. I have a box that I keep only for this purpose. It has a hole in the top of it and I place a plastic bag beneath the hole. I place the bird on the other side outside the bag and spray Ether (Starting Fluid) into the bag through the hole. The Ether puts them to sleep painlessly and the prolonged over exposure to the fumes finishes the job. You would want to make sure the Ether goes in the bag and not spray directly onto the bird. I haven't experienced it myself but I imagine it would burn badly if it were to get in their eyes. The reason I use this method is that it's painless.
If you felt he is too large for this method, what I would do is use a 22 Cal. with Snake Shot in it at close range to the back of the head. While not totally painless, it would be quick.
Again, I feel badly for you,
David