Just a random update:
Inexplicably, my game started saving again and I was able to move past the 'point of no return' that I was having earlier. I didn't do anything different (didn't take any mods out or put any back in), and tried just the basic 'save' function and it's worked. I've been able to play to the end of the day whereas previously it was stopping in the morning.
Whilst it's saving properly, I've decided to 'save as' and create a new save file, in the hopes that maybe that helps. I'm not going to hold my breath, though, as I know for a fact it wasn't just this family or this specific save file, because the problem still happened even when I created a brand new household in a brand new save file just to test the issue.
I'll keep playing to see if the issue arises again, and give an update here if so. It feels like this issue can't be specific to one particular mod or save file as, like I said, it still happened with no mods and in a brand new save. Hopefully there's some kind of fix that could come in the form of a patch or update etc seeing as so many players across platforms and save files are having the same, or at least similar, issue.