Would Unity candidates or the eventual nominees be precluded from also seeking the nomination of one of the major parties?
I used to live in New York, and as I recall the Democratic nominees would often also be listed on the ballot separately as nominees of the Liberal Party, and the Republican nominees would likewise often be listed as the Conservative slate. It was essentially immaterial which of the two slates you voted for, as long as the minor parties received enough votes to remain on the ballot next time around.
However, in this case what would there be to prevent the Unity Presidential candidate winding up with two VP candidates -- one on the Unity ticket, the other on the ticket of the major party? Indeed, what would prevent one person from being simultaneously the Unity Presidential candidate and the VP candidate of one of the major parties? (The latter possibility is pretty farfetched; the former somewhat less so.)