I probably won't even have Internet access for the next few days so screw it, I'll keep this as brief and simple as possible so we can go from there. The in-game context goes as follows.
1: All of the statements about AD's superiority to space and time come from the games. Not the Twitter post. It's not as explicitly 5D as the latter, but it can still mean the same thing, especially with more context and the fact that a superiority is in fact mentioned.
2: A higher space containing the lower one within itself is already a good start, and the proof of that being the case also comes from the games, including the instances of AD being used as a gateway for pretty much every space-time coordinate, including those in the past of a "distant realm"
3: One such piece of evidence is in Kirby RtDl. Not only can the universe Kirby and co previously visited be seen inside of AD, but said universes are portrayed as transparent, fading pictures. As if they were of a lower level of existence or 2D by comparison.
All of this is to say that even though my argument ultimately stems from the Twitter statement, it's not like the possibility of a higher dimensionality for AD was unheard of before it. This so called tertiary source ultimately serves to confirm what would otherwise just be a possible hypothesis. That's why analyzing the linguistics of it is so important. If my translation is correct, so is the upgrade.
The thing is though, that this isn't "my translation" I had help from an actual Japanese speaker. No one currently here is as qualified as he is, including me. It's my word against yours and we're going nowhere, so I'll send invites to some of you so you can talk to him directly. How does that sound? I'll probably send them to you one at a time as to not overwhelm him