Hence my question: if I uninstall and reinstall FS Labs and GSX, is there any chance that this will solve the problem?
I don't think reinstalling GSX would make any difference. The key issue is you are not getting this line in the log:
"Number of passengers provided by addon is ..."
GSX writes this, when it sees the FSDT_GSX_NUMPASSENGERS LVar is not 0, which tells GSX it should not try to figure out the number of passengers, but should take it from an external app. Instead, your log shows the variable IS 0, so GSX reverts to the default calculation based on payload.
As I've said, the only time where the variable can be written by GSX, is when reading a Simbrief flightplan, which wasn't your case, since your log shows Simbrief wasn't used because your airplane doesn't have an ICAO code in its profile. And even if Simbrief was used (it wasn't) for the variable to be 0, it would have required a flightplan with 0 passengers anyway.
Do you have something to check the value of the LVariable yourself, like Lorby's Axes and Ohs or FSUIPC? You might be able to monitor the value of FSDT_GSX_NUMPASSENGERS, and see if it ever gets set correctly and/or, when it goes back to 0.