As silly as it sounds, it would probably resolve this issue perfectly. As I remember, I always got the login prompt at roughly the exact same time into the meeting, suggesting it's just set to expire after a certain amount of whole days.

Google internally is well aware of this, and in fact one internal tool most engineers use actually has an expiry a few hours short of 24h simply to prevent exactly this issue.

But it's not fixed because....?

I'd suggest changing it by a 12 hour delta. Then you are likely to start encountering it at the beginning of your day instead of in the middle of anything.