Halal is standard dietary law. Different sects all follow it, when it comes to the slaughter of non-aquatic meat.
It’s like Kosher. Some liberal Jews disregard it, but the laws of Kosher do not change. This group is what the Muslims in my area (Detroit) use as a guide. It’s not about the different sects.
They're mostly engineers or guys with doctorates ~ and they follow a practical sort of Halal avoiding pork (which your list does help them do).
Still, we've had the nearby Afghan community shoot some Iranians to death over what can only be described as religious differences.
As long as the crowd around Detroit continues to collect in like minded ethnocentric communities you will miss out on that sort of thing.
But here if you want to make sure your meat was slaughtered according to the most rigorous Halal standard you need to go visit the same farm the Orthodox Jews do where they are equipped to do slaughtering on site. Otherwise you get what you get.