@interfluidity no mention of #rankedChoice?
Wouldn't having three choices be just as good? Approval voting, as you have described it, still involves a binary approve/disapprove, and I am afraid it would not be enough to break up the parties. Just more candidates divided along the same lines? I want to avoid that binary choice.
I would add to #rcv a single vote against someone, to be counted along with first choices, increasing the likelihood that a first choice winner would not be divisive.