It looks like you just attached the router log. Can you send us your full log? There are some different ways to access and share Local Logs. For us to be able to troubleshoot thoroughly, please click the Download Local Logs button from the Support tab in Local. This will generate a zip archive that contains the Local log along with some other diagnostic information to help quickly zero in on any issues that Local is encountering.
Also, does changing your Router Mode have any impact? Go to Local>Settings>Advanced to find this.
Bingo. So what we were looking for here was to see when sites are stopped and Local is properly shut down if there are still programs running on ports 80 and 443. These may be conflicting with Local or the system may be reporting Local is still running.
If your antivirus is shut down but still using ports, then you kill that process (or processes) by running taskkill /F /pid XXX
XXX is the PID number of that process which you should see in the column on the far right.
After that, you should be able to retry. Keep us posted if you have any questions or continuing issues.