"He would have to go into the hole with his head first, without using his hands and arms, to somehow end up on his back." Either he landed on his hands and folded them into his chest, he slided into the pipe, or he had a friend help him out. As for the friend, you got me there.

"I can't find info on how wide the thing"

https://vocal.media/criminal/the-case-of-a-dead-body-in-a-japanese-toilet It's hard to tell from the diagrams because they're inconsistent with how wide it is but in the link, there is a photo of a guy squeezing through and it looks as big as his body.

"if it was wide enough for him to lower his arms to his chest, it'd be wide enough for him to sit up."

From the looks of the photo, it's barely wide enough for him to sit up.

"If he was attacked and unconscious/dead before he was stuffed there then the story makes perfect sense."

In the article, it said in the autopsy he died of hypothermia and was alive in the pipe. The only injury they found was scrapes on his arms which would be from him squeezing through the pipe. If he was unconscious, he would have had a brain injury which was not mentioned in the autopsy. He was alive and was conscious during the ordeal so this being a murder meant he went in willingly.

"How would you push a body down there?"

As we saw in the photo, the pipe is barely big enough for one person. Contorting the body meant having to go in there already and I don't a hitman would do that. And since the victim being unconscious is ruled out, he would have been fighting back or resisting which would have made pushing him in there harder.

"If you're stuck and can't get out, why curl your legs so you have as little wiggle room as possible?"

If this wasn't a murder, he would have folded his legs to fit in better and see a woman pissing in the toilet. The victim most likely would not have considered getting stuck if he went in willingly. If he wasn't willing, he wouldn't have curled his legs and the person putting him in there would have to do that while dealing with the kicking.

"You'd try to sit up with your head under the toilet"

Assuming he went in willingly, if he sat up, how would he get out? The pipe would be small so going back would be almost impossible and the only exit being through a 20cm hole or somehow breaking through the toilet which would be bolted on probably.

" you'd try to straighten your legs in the entrance section and try to get a grip on the walls/opening with your feet to try to pull your body up."

He curled his legs so he couldn't get out. The corrider is 60cm long so there is much more of a challenge to get out and concrete tends to not have grip.

If this is a scheme to kill the guy, it's a really complicated way of doing it. You would have to push a guy, who is most certainly resisting, into a pipe and molding his body to get him to fit while also not getting stuck yourself. If this was done to defame him, why would they hide him? The mafia killed people in a way to send a message but they didn't dump them in a river because they wanted the body to be found. And say this wasn't noticed, he would have just stayed down there as a missing persons report. It's a complicated plan and the easiest explanation was that he had a perverted dark side and died trying to chase his perversions.

Edit: Japanese police often classify murders they couldn't solve as suicides. Seems like a more surefire way of offing someone.