A no-nonsense guide to the "SAVE" and "LOAD" functionality inside of Chapter 5
To be honest, this mechanic is a little tricky to figure out. Sure was for me. So here's a rundown of where you need to save/load, and where.
Note: Every save requires you to SAVE Saturday. Saving any of the other characters doesn't progress you, but I wouldn't be surprised if you would need to at some point during the next part of the Final Chapter.

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In relation to the provided hint: When it talks about listening to the burdened girl, this means you need to pay attention to the dialogue near the end of X6.
Extra Hint: You will need to restart your game at some point.
Solution: After Dawn fires the gun, there will be dialogue that says something along the line of "RESTART TVO NOW!!". That's your cue to ALT+F4 and relaunch the game.

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This is when the game actually explains to you how to properly SAVE and LOAD.
SAVE POINT: Inside of X7, as Saturday calls for Allison in the burning building. The screen should be black.
LOAD POINT: Inside of X6, as the dialogue box mentioning the earthquake with a red glitchy screen appears.

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SAVE POINT: Any time at 2:30AM (in-game) should work for this.
LOAD POINT: In X8-A, when Saturday mentions how similar the office is to her dad's office in the real world.
Extra: If you're stuck after doing this on the part where it tells you to SAVE Saturday, try to SAVE then immediately LOAD. Worked for me.

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SAVE POINT: At the black screen at the end of X9.
LOAD POINT: Go back to Chapter 2, Episode 8. Immediately LOAD. (Sometimes it flashes red but it should work. If not on 1st dialogue, try it at the 2nd dialogue before she wakes up.)
Continue through Chapter 2, Episode 8 on this alternative route.
SAVE POINT 2: At the end of Chapter 2, Episode 8
LOAD POINT 2: At X9-A, when Saturday exclaims something about "We can load!".

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Don't need to spoiler this, just read X10-A, X10-B, X10-C. The lock will automatically unlock (this shouldn't be an issue if you're actually reading the story. You really should read the story.)

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Uhh, cool. If this is posted a bit too early for any of the dev's likings (for whatever reason), just reach out to me here and I'll take this down. Otherwise, happy Saving (and Loading)!

- slax