So when you call in to tech support, they are reading off a script. The script walks you through the most common resolutions to people's problems ("Have you tried turning it off and then on again?"), and is entirely useless if you're at all technically competent. If you're like me, your support calls usually end up being exercises in absurdity - can I go along with the script long enough for them to become convinced that they should put me through to someone competent?
Randall Munroe had the right idea. He just didn't take it far enough. It would be really great if everybody implemented backdoors for techies, but really. If we want backdoors, we're going to have to make them ourselves.
What we should do is make a repository of tech support counter-scripts. Let's say (as in the linked xkcd) that you know exactly what the problem with your internet connection is, and you want to minimize the time it takes to convince the person on the other end of the line to just fix your problem. We could crowdsource it, and have everybody who tries the script try tweaking it on actual calls, and iterate toward the fastest way to resolve a given situation.
So here's the really cool bit. We also include some distinctive phrases in the scripts (backdoors, if you will), so that after a while the support people will catch on to what we're doing. At that point, they have a choice: they can either look up the backdoor phrase in the counter-script archive, and find out what specific problem we're trying to get them to solve; or, they could adjust their scripts to counter the counter-script.
Few people are stupid enough to choose a fight against a crowd (just ask /b/), so eventually they will add the backdoor phrases to their scripts, with the instructions that we wanted them to have in the first place. In effect, we'd be social engineering the backdoors into the support system ourselves. Pretty cool, huh? :D