I sincerely apologize. This is a good website and I hope you don't judge all of BYC by my response. It does seem like your mind was made up before you posted your inquiry, so I'll unsubscribe and let you get some help from others. Again, my apologies.
Coming to you live from Oleo Acres, the Cheaper Spread!
I know this is an old post, however I crushed a benadryl mixed it with very little water and a very little yogurt and put it in a syringe and gave her little at a time. Once she took it all she became very relaxed held her and she basically went right to sleep. She did do the the normal flapping of her wings right at the end or at least tried, I had her wrapped in a towel. Was as humane as I could! Hope this helps! Couldn't watch her suffering any longer!
Metacam (meloxicam) is a non-steroidal anti-inflammatory used to treat pain and inflammation. It is very unlikely to cause sedation, nor unconsciousness or death. It would cause kidney failure in high enough doses (read over dosing).
The view from the vet community is still that a well performed cervical dislocation is the most humane, second to lethal injection (if not for consumption).