I will never vote for a non-Libertarian whether or not they are a member of the Free State Project.
FreedomRoad makes a good point about this, Radar. Personally, I believe that many more voters would be open to libertarian ideas, as well as the LP, if it were not for the reputation that libertarians have gained due to some loonies who sought refuge under the libertarian label (and various single issue fixations on the part of some LP'ers as well).
If we are successful in the chosen state, then libertarianism and the LP will be better understood and more widely accepted in time. In the beginning though, we're going to have deal with voters who would not think to vote for libertarian candidates for any wide variety of reasons. The process of educating the public on the true nature of libertarianism, although it is certainly possible, is going to take a considerable amount of time, and if we limit ourselves to LP activism only, we will lose ground to statist forces operating within the two major parties.
I'd rather see us spread out through a state's political infrastructure (where feasible, of course) and making headway on all available fronts, as opposed to isolating our activities to one minor party and struggling to be understood and accepted while our opposition governs.