I wish that the simulator worked in reverse, i.e. instead of showing for which center-of-opinions a given candidate would win, it would show given a distribution-of-opinion, how should a candidate position themselves to win?

This is a much more interesting question to me, first because the candidates' positions are more mutable than the voters' opinions and second because as someone whose political opinions are often non-aligned with major parties, I really wish that there was an incentive for viable 3rd-party candidates to give a voice to my views. The ncase.me simulator linked elsewhere on this thread seems more useful:

https://ncase.me/ballot/