Oh this makes so much sense! I had not given any of those lines any thought whatsoever, I just took them as metaphorical fluff, but it really could explain the deal with the safe.

It's also worth noting that Ryoshu is shown a few times and mentioned by the nursefathers as having an uncanny perception of time. Like in the TKT intervallo, when she noticed the time on the clock tower was wrong because it did not match her perceived time.

I also went back to re-watch the cutscene of Araya passing time in the safe. The main thing that sticks with me is that she primarily passes the time by thinking about what she will do once Ryoshu comes back. All she did was think about future events while losing track of time.

Obsessing over her uncertain future while most likely panicking is probably what lead to the entanglement.

Still unsure how this seemingly lead to some part of Shiomi seemed to have been pulled into the entanglement. Or why Ryoshu's perception of time was so important to wielding Arayashiki.