I did not need to because voters would only bullet vote if either
(1) they genuinely preferred one front runner over every other candidate,
(2) they preferred one front runner over every other candidate they knew about (which is not many), or
(3) they made a tactical error.
I doubt that many people would actually be in category 3, because given the design of Score Voting it is hard not to give a score greater than 0 for people you like. So more likely the voter just has not researched the third parties, making him or her in category 2.
As for 2 itself, this category will gradually erode away as third parties gain more coverage. (Also people will likely out third parties as no opinion, so third parties may actually win quickly... or slowly, in harsh-blue or harsh-red areas.
Sorry about this rushed comment.