Many thanks for your post, TokyoSleuth! And very kind of you to say about the podcast, so glad you enjoyed it. Apologies for the delayed response, I've been in South America. Anyhow, taking your points in turn:
*Filling the bath tub 1: I think what's weird about this is filling it with items belonging to the family. Papers, ID cards, so on. I can only assume he wanted a place to sort through it and toss what did interest him. But then that suggests he's LOOKING FOR something. And if so, that hints at a motive potentially. And if after 22 years and thousands upon thousands of TMPD man hours they haven't shared that theory, then I'm doubtful... (It's possible they don't want to. But at this stage, frankly, that would be ridiculous).
*The outfit worn by the killer: I don't find it unusual, either. Whether the year 2000 or even today. What is interesting is 1) where he bought certain things from, such as his top from M/X. E.G., despite its rarity, the police could only ever track down one or two owners. And 2) the fact that he left most of it there. It makes total sense if it's covered in blood. But on the other hand, in the dark of night, he could've just made a cursory attempt to clean that off his dark jacket, zip it up, and hurry away. He chooses not to do that, steals a sweater belonging to Mikio, and leaves his stuff there. That tells me either he didn't GAF about the cops tracing his items or he had no choice because his clothes were beyond salvage. Alternatively, as mentioned elsewhere in this thread, he's not in his right mind. Maybe a combination.
*The airman theory: I've seen the TMPD / local media blame crime on foreigners many times. But they actually didn't do that here. At least not the TMPD. If you look at their page on this crime on the TMPD website, nowhere does it mention anything about this. They actually didn't WANT Wikipedia to mention the potential DNA 'link' to a Korean (it really isn't, as covered several times throughout this thread) precisely because the science was junk. A chance of 1 in 4 Korean, 1 in 10 Chinese, and 1 in 13 Japanese -- this simply isn't evidence. There's a chance my Aunt Hilda could've been my Uncle Harry etc. The reason why the USAF theory (or son of USAF member most likely) could be credible is that there is sand from a part of the Californian desert where there is very little else beyond the USAF base. And it just seems to be a coincidence that thousands upon thousands of miles away, there is another USAF base relatively close to the crime scene. If you delete USAF, there isn't a solid explanation for it. That's not a smoking gun, as I've said many times, but it's also unexplained by the TMPD. Post-podcast, our sand specialist confirmed that there is no way the TMPD could confuse sand from Japan (such as from Miura) with sand near Edwards AB.
RE: your distances, I'm a bit confused because my maps are telling me different? From Yokota AB West Entrace to Fussa Station is like 1km (maybe 10 mins walking?) and then it's a little over an hour on public transport to Soshigaya Park. I've done that route myself and can vouch. Also, from Fussa to Ogikubo (the area I believe most likely for a first contact point between the killer in the airman theory and the Miyazawas) it's under an hour. According to the family, the Miyazawas did their shopping there and it's also the location of M/X and various other stores selling items of clothing the killer left behind. So again, another coincidence. Zama is another option, of course, one we didn't look at for time reasons in the podcast. But google is telling me it's 1 hour 20 mins from Zama to Soshigaya Park via buses and trains.
Also, re: the folding of clothes, where did you read the killer did that? I don't think that's ever been confirmed, only ever rumoured. In any case, the Chief rejected the idea and simply said his clothes were 'left' behind. The wrapping of the knife was something that the police looked at being 'Chinese' or 'Filipino', so again, I don't think that's exactly concrete (not there is anything concrete in this case except for his DNA). And as for barley tea, I have one British parent and one Spanish and I always drink it whenever I'm in Japan. So sure, it could well point to a Japanese person. But it also could well not.
The Californian Sand: Simply put, the TMPD refuse to tell us where this clue came from but also refuse to discount it. The Chief was VERY vague about it to me when he was vague about almost nothing else and very forthcoming. He made it clear he suspects the killer was Japanese until there is something more against the idea. Which is totally fair and logical. But then we are talking about a 'teenaged' killer who somehow transported a Japanese bag to the middle of nowhere in the Mojave Desert, picked up some sand, then brought it back to suburban Tokyo... by mistake? It's possible he stole the bag as I've said many times. But some of his clothes are brand new (and not cheap) so he would have to have stolen a bag (without it being reported) from someone who had been to Edwards or to the nearby desert. It's possible, of course. But like many have said, it feels a lot more likely it simply belonged to him and he left it behind like everything else. So, in short, I think the sand thing was leaked in the same way the 'mixed' DNA thing was leaked. The TMPD mention neither on their website. I have no idea why, at this point. Nor do I understand why they don't do further testing on the DNA, but that's a whole other can of worms... But in short, until proved otherwise, I do believe this is concrete evidence. FAR more concrete than BS footprint in blood evidence that the TMPD used to go to Korea with. Despite the shoes also being available in various other countries...
*Bath 2: I agree with you, the window would have been very difficult to enter the house from and the TMPD said themselves there were no fibres in the frame. Then again, they can't prove he came through the front door. That leaves the balcony which they have never mentioned. The front door for exit would've meant blood though and there was none at the door. So either he found some way of cleaning his tracks from Mikio's body to exiting the house or he left some other way. Possibly the balcony. It's maddening that 22 years after the case, the investigators can still be so unsure about something so basic.
*Timeline: We simply don't know the timeline for sure other than the TMPD say Rei was first based on him having no blood on his body (though there was a lot of blood in his room on the floor, presumably from the killer pacing around afterwards). It seems impossible the killer could've gone up the ladder to the attic to attack mother and daughter with Mikio still downstairs on the computer and him not hearing. Those wooden pull-down ladders are noisy, as well as the house in general. I think Mikio would've even heard the killer's footfalls leaving the room. I think in the darkened panic, Niina and Yasuko, who were likely asleep, simply didn't know what to do. They were both stabbed and in their shock, probably assumed that the killer leaving was because he was leaving. Not going to look for another knife. I'm not sure that speculating what makes sense while bleeding and terrified after being attacked in your own home is something that is particularly fruitful. Maybe their actions are confusing because they were confused?
Cat killings: I don't have a link to the 2chan post but I'm fairly certain it's been posted in the thread previously. It's somewhere in my research files but I don't have them to hand. The Chief seemed convinced the ones occurring at the time of the murders were NOT linked to the murders though and I'm fairly sure the guy was caught. (Given Japan's conviction rate, though, there's no certainty it was the actual culprit). But for sure, the killer would almost certainly have acted out violently in some form or another. This was part of what first made me think of a USAF airman's son -- the TMPD wouldn't have access to disciplinary files in the high school on-base etc. It's quite possible the killer did act out at school but they just simply didn't know about it. Alternatively, this simply happened in another country and it never was connected by the TMPD (or the killer simply got away that past behaviour as well as these murders). And I also agree, it's more likely the killer had some knowledge of the area. To carry out such violence in an unfamiliar area feels like a much bigger risk than doing it somewhere he knows. Then again, he took some wild risks so who knows.
Also, going back to the 2Chan post. It's worth seeking out because, although the Chief discounted it as BS basically, the poster does make an uncanny prediction. If nothing else, it's a chilling guess...
*RE: the family hiding their son's actions, hard agree. Especially if you thought he could be facing the death penalty and, as I understand it, 4 murders of this nature is the noose almost guaranteed. Of course, sometimes, people simply don't want to see the obvious. So he could've said he was attacked and picked up a sweater from the trash, who knows...
Thanks again for your great post, TS. Let me know if you have any other thoughts!