As for dealing with our current state however, it can be useful to remember that the Republican Party began with people "wasting" their votes on them as a third-party choice, to begin with. They WERE the third-party candidates alongside the "only two choices" of the Democrats and the Whigs.
Not exactly. In the parts of the country where either the Republican Party or the America/Know-Nothing Party (the latter of which would ultimately be absorbed by the former) they were running as one of the top two parties due to either support in that particular area for Abolitionism or Nativism respectively. District by district you still had what amounted to a two party system, in some districts one of those parties replaced the Whigs and in others the Democrats. (It's often forgotten that both the Democrats and the Whigs were divided over the slavery issue, the Democrats base of support in the South as well as their support from Irish and German immigrants allowed them to survive that division somewhat intact.)
It's virtually impossible in a system which uses "first past the post" voting to maintain more than two viable parties for more than election cycle or two. Almost inevitably, those supporting the candidates coming 2nd and 3rd will be closer in their position than the candidate which emerges as the winner and will choose to compromise rather than continuing to lose. In the US system this extends out even further though because we have unitary executives at both the state and national level which extends this inability to maintain more than 2 parties past the individual district out to the state and ultimately the national level.
Basically, in the US system, similar to what happened in the 1850s to break the present two party system would require there to be a major issue which, despite being supported by a large portion of the population
to the point where they will vote on it as a single issue, isn't supported by either major party. At the present time there simply exists no such issue. The major parties have simply proven since that time to be too adept at co-opting whatever issue is being brought forward by a third party once it gains that level of support from an even remotely sizable portion of the American public.
Which actually gets to what the real function of the 3rd parties and independent candidates has been for the past 150 years or so, and that's to push a particular issue to the point where it gets adopted by one or the other of the major parties. The most recent example of this would be Ross Perot's run in 1992 which led to, for at least a brief period of time, both parties working towards reducing the federal deficit.
At the present though, there don't exist any third parties which are actually doing this. The largest of the 3rd parties (Libertarian, Green, and Constitution) have broad agendas supported by only a tiny fraction of the US public. Which is essentially the polar opposite of what is actually effective.