Seventh Day Adventists go one step further. Since the late 1860s the Adventist Church has advocated a vegetarian diet. In 1938 the SDA Church compiled Ellen White's writings on health into a book entitled 'Counsels on Diets and Foods'. Here are two quotes on the subject of eating meat:
"When the message comes to those who have not heard the truth for this time, they see that a great reformation must take place in their diet. They see that they must put away flesh food, because it creates an appetite for liquor, and fills the system with disease. By meat eating, the physical, mental, and moral powers are weakened. Man is built up from that which he eats. Animal passions bear sway as the result of meat eating, tobacco using, and liquor drinking." (p. 268-269)
"As a general thing, the Lord did not provide His people with flesh meat in the desert, because He knew that the use of this diet would create disease and insubordination." (p. 375)
No reference is made to Genesis 9:3-4 where God gives Noah permission to eat meat, but with this proviso:
"Everything that lives and moves will be food for you. Just as I gave you the green plants, I now give you everything. But you must not eat meat that has its lifeblood still in it."
There may be other Christian denominations that prohibit the eating of meat from strangled animals, but it would take a great deal of time and effort to track them down.
As for Jehovah's Witnesses, while they are asked not to eat meat that has been strangled, they are not under any obligation to make enquiries from the butcher to ensure the animal's blood has been drained (that it was not strangled). I believe this is left as a matter of conscience and is not a hard and fast rule.
Edit - Additional information on Christian denominations (other than Jehovah's Witnesses) who uphold the prohibition on eating the meat of strangled animals:
The Armenian Apostolic Church observe rituals similar to Jewish kosher slaughter (second paragraph): https://www.revolvy.com/main/index.php?s=Christian+dietary+laws
The Iglesia Ni Cristo (Church of Christ) forbids the eating of meat from strangled animals: https://iglesianicristoreadme.blogspot.com/2009/08/eating-animals-blood.html#.WxY1B0gvy00
Apparently, the Catholic Church can allow the eating of meat from strangled animals: http://newtheologicalmovement.blogspot.com/2016/05/the-church-can-allow-eating-strangled.html