You don’t have to like the question, but it is what it is. As for a real-world example, Teddy Roosevelt did pretty well. He beat one major party candidate, though he obviously didn’t beat both. Personally, I think Jeruba seems like a pretty good candidate for these modern times. But alternatively, we could just take someone from Hollywood who isn’t reviled by either side and fill him full of platitudes. It worked for Reagan, after all.
I don’t disagree with being strategic with one’s vote. I vote for third party candidates when there’s no chance my preferred major party candidate is going to lose (or, in the case of presidential elections, will lose my state). I also vote for them when they have a real chance of winning, which has worked out well for me at the local level, or when neither major party candidate is offensive to me.
I also agree that democracy works on compromise. I’m not at all offended by someone I voted for doing something I disagree with, especially if I knew upfront that s/he might do so. That said, I see no reason not to support people I agree with even more or policies that make it possible for them to participate in the process. A two party system is a travesty in any country and contrary to the basic sentiments on which the US in particular was founded. I accept that it is presently a reality, but that doesn’t mean I have to help perpetuate it.