I agree that having your code as a module or not does not make a big difference here, but you should be able to "diddle the logging to appropriate levels in the .t". Is it not possible to turn off logging from the test script for your negative tests, and then turn it back on for the others?
Re^3: Strategy for conditional logging in tests
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Maybe there is something I do not understand about Log4Perl, but could you not call Log::Log4perl->appender_thresholds_adjust from within your test script? The whole point of a configurable logging framework seems to be that you can configure logging from outside of the code that does the actual logging.