What alternative ways can you think of to handle making legislation and passing laws that would negate the increasingly polarized political climate that is happening in more and more countries?
You'll probably need to think beyond liberal dogma if you want to solve a problem with liberalism. "Paying for something is speech and therefore unimpeachable" is an insane thing to take as a fundamental element of how society is run when the end result is so obviously and demonstrably the rich using that ruling (which was always made for them) to buy elections.
People want to find some policy wonk solution to these fundamental problems ("Oh! Sortition fixes everything! Wait, maybe a parliamentary system. Ooh, ooh, how about . . .") but they are just red herrings, silly schemes that distract you from critical thought about the assumptions that brought you here.
I hear what you are saying, but that isn't campaign finance reform. Redefining what is protected speech seems like a prerequisite to campaign finance reform. And that does sound like a good idea.
It certainly would help. But can it be leveraged to deal with the media which makes money polarizing the issues? If you don't fix that too I am not sure the problem will really be solved.