Try changing the time zone on your computers operating system.
I know that if the time zone in the computers operating system is changed,
that changes the browser time zone.
Other than that, I don't have any other guesses of how to change the time zone returned by:
e.userTimezone
If you change the time zone on
your computers operating system,
you may eventually be detected as a potential security risk.
Regardless of whether you are or not.
I'm assuming that you want to do testing for different time zones for your add-on.