The best way to move America in a given direction in Nolan space is to aggregate into the same party everyone who prefers that direction. In any multi-dimensional analysis of American's political views, Americans cluster mostly in the 2-D plane defined by the Nolan chart, and even more so along the left-right diagonal of the Nolan plane. As noted by Duverger's "Law" (http://en.wikipedia.org/wiki/Duvergers_Law), this in combination with plurality voting laws means that successful third parties cannot arise along that diagonal without being co-opted by the two existing major parties already encamped on that line.
The Authoritarian/Populist quadrant has been kept mostly infertile for a third party by Republican co-opting. Similarly, Republican electoral success from the Right quadrant has led extreme rightists to work from within the GOP instead of from without. The Greens have embarrassed the LP by building the strongest third party in a quadrant dominated by the Democratic Party and its special-interest rent-seeking patronage machine. The LP has seriously botched its opportunity to build a third party in the utterly vacant North quadrant.
To start a new party in Nolan quadrant that already has one is to indulge in the same sort of moral exhibitionism that already is the LP's primary problem. It's just as possible to waste political effort exhibiting one's moderateness as it is to do so exhibiting one's extremism. Thanks to its self-marginalization, the LP has nowhere near the negative approval ratings that would be required for a new libertarian party to be our smartest move. Until that happens, the worst-case strategy for wise non-anarchist libertarians under a puritarian resurgence would be to clog the LP member rolls with lots of low-effort moderates, bide our time until we can expand the tent again, and continue to help libertarian efforts in other parties and especially in non-party institutions.