I'm not sure that's true, because they will still have to appease their other constituents in the existing base by making compromises (that will make you not want to vote for them again)
Well, it wouldn't be easy, and I think there's a reason we don't see any meaningful electoral reform, but I don't see another way.
Perhaps one could convince the major parties to support electoral reform by constantly hitting them with spoiling candidates. Run left-wing independents in districts which are typically safe for Democrats but still reasonably close. Run right-wing independents in districts which are close but Republican. If you can get both major parties to get fed up with losing seemingly safe seats due to the first-past-the-post system, that might get them to change it.
