I've worked in a family member's small meat processing facility, and they offered slaughtering for hogs and cattle. The method there was to use a captive bolt gun - basically a gun, but instead of propelling a bullet from a cartridge, it used .25 caliber blanks to push a metal piston ~6" out the end. It was quiet enough that no hearing protection was required.
The process was basically: * animals in queue were kept outside, in a covered holding area, separated from the kill floor by a concrete block wall * a chute door was manually opened to allow a single animal into the building * the animal was killed by placing the bolt gun on the head, driving the piston and parts of the skull into its brain * the carcass was raise with a winch and hooked to an overhead rail system.
The rail system was used throughout the operation, from slaughter to when the carcass was broken down into parts. They didn't have enough employees to always have every workstation in operation, so there were freezers throughout the area that would be used to store the carcasses while slaughtering was taking place. Basically each one would be skinned, dressed, and stored in a freezer. Once slaughter was complete, there'd be a similar setup to break the animals down into quarters or large cuts (depending on the customer's order), and yet another to butcher from quarters into packaged cuts like you'd find in a store. Making finished products like sausages would be another workflow still.
My understanding is that this operation is pretty typical of small meat processors, and every one that I've visited seems to follow a similar pattern.
From an empathetic perspective, it honestly seems fairly optimal to me. Yes, the animals are uncomfortable because they're in unfamiliar surroundings, but they're insulated from the sights and sounds of the kill floor until literally moments before they're killed. I don't think oxygen deprivation is necessarily any better in that respect. I suspect it's more easily scaled, requires less labor per animal, and cheaper overall once a certain volume is reached.
ETA:
To be clear, I am not making a political or moral statement here. My background is very different from most people that I've encountered in tech, and I'm only sharing my experiences here to contribute to the conversation in a way that I expect isn't possible for most of us.
I assume that most people reading HN haven't spent time in places like this, much less spent participated in the process.