I wonder if you could form a mathematical model of which districts would be most amenable to a dedicated 3rd party challenger. It seems like you'd want a district which is a "safe seat" (if there is a serious R/D contest in the district, people will want to avoid "throwing away their votes" by voting for a 3rd party). But you'd also want to identify a district where people are dissatisfied with their elected representative anyways. Ideally the elected representative is a significant distance from the median voter.

Maybe a good metric would be the ratio of primary ballots cast to general election ballots cast. If a small number of extremist primary voters are de facto selecting the candidate that will win the general and get the "safe seat", that suggests an opportunity for disruption by being a high profile 3rd party candidate who's just a bit more moderate than candidates the extremists select (more appealing to the median voter).

Another idea is to reach out to a bunch of independent candidates and try to recruit them for your new party to work towards critical mass.