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As an alternative to the appalling arrangements at the tube station, you might consider the (somewhat) less bad alternative of taking the 84 bus from the train station at New Barnet. That's hardly brilliant. The train arrives every 20 minutes, and the bus leaves every 15, so synchronisation isn't perfect.
If you pick the bus that apparently leaves exactly when the train arrives, you will see your bus leaving the station forecourt, just as you are climbing the steps up from the station platform.