AD, you seem to be thinking only on the grand scale: Local candidates don't really get that much help from the parties; basically only the training of aides and other assistants & gofers. If I'm a cop, and have served fifteen years, and decided to run for Deputy Sheriff, it wouldn't really matter to what party I subscribe, because it's not that hotly contested an office. Let's say that I win the office, because it could happen, and over the next ten to twenty years I get a bunch of party compatriots to run for the school board, the county commission, treasurer, etc., all while serving as Sheriff, and then throw in my hat for the election for Mayor or County Commissioner. Let's also say I do this without any major controversies striking me or my compatriots. See the endorsements I'd have from the local non-big-two officials, whose names and records are known? See the corporate backing I'd have by tying myself into the community and associating my performance with my party? Let's say I've portrayed myself as Libertarian the whole time, but made a little deal of party to the people, and a big deal of issues, and let the people settle it at the polls. See how the big parties could be eroded from the edges?
Imagine this happening in Tempe, Dayton, Albany, Hartford, Redmond, San Bernadino, Missoula, etc. See how small cities could be good launching points for small parties? That's how the big parties could be overthrown: in small doses over a long time. Another twenty years could see a multi-party, coalition-type Congress which safeguards civil and human rights while neither overregulating nor underregulating businesses, made up of a big group of people that would make unnecessary war damned near impossible.