Yeah, I can see most people can agree on feeling that the two big parties don't meet their needs, but I highly doubt they agree on what that third party should be. And if that's the case there's a real "you go first" problem under FPTP for voting for new parties, because otherwise you've just given the established party on the opposite side to your own views an effective boost by switching from your traditional party to one that meets your views better.

You really need at least ranked voting and ideally multi-seat PR to get out of that, which is hard as it's against the interests of the two big parties.

That said, looking at the UK there does seem to be a renewed interest in moving away from FPTP in their Labour Party despite it being nominally against the parties interests, so maybe there's a way to get movement on that?