My preferred general approach is that the answer to speech you don't like is more speech. Very specifically, large numbers of people can in turn collectively buy their own "free speech" through various forms of non-profits. Right now, compare the 5 million members of the NRA vs. Michael Bloomberg, who is the
only person currently putting serious money into gun control.
In a way, that supports your case, in the Colorado, Washington and Oregon wins he's achieved (through non-profits fronts he's established, after Mayors Against Illegal Guns became so notorious for the number of criminal mayors in it). But not generally, nationally the needle hasn't moved aside from Obama and Hillary! publicly calling for the confiscation of the nation's handguns and semi-auto long guns (!).
But our response is not to try to muzzle him, let alone support a law like McCain-Feingold which muzzled the NRA and therefore its 5 million members working in collective action prior to it being spiked by Citizens United.
I'll also note that money only gets you a hearing, I simply don't believe that big money can "dominate the political dialog and crowd out dissenting voices who have less money" without concurrent capture of gatekeepers (like the Federal government in the case of McCain-Feingold...). The examples are legion, the latest being ¡Jeb! Bush's total failure to gain any traction outside of big money sources.
(I recently came across an analysis that to win the Presidency, you've got to do well at both getting "big" and "small" money. Hmmm, like Obama did. By that metric, watch Cruz, and of course Trump is a wildcard, not needing either and currently not playing that game at all.)