I think I have the same issue, but I did not think of it as an issue with kill switches, for me it is a more general problem that the mobile internet connection sometimes stops working and when that happens the L5 is unable to recover from that problem, until reboot. But the way you see it could be a better way to investigate since you get the same behavior every time.
Anyway, it could be related to this:
A way to troubleshoot I think would be to turn on ModemManager debug output by changing a line in the /lib/systemd/system/ModemManager.service file like this:
ExecStart=/usr/sbin/ModemManager
-->
ExecStart=/usr/sbin/ModemManager --debug
and then look at sudo journalctl output around the time when mobile internet connection fails.