You have yet to make an argument how campaign finance reform would change any of the above.
- No more gerrymandering
- Mandatory voting(You can still vote for nobody, but you have to go to a polling station)
- Voting always on a weekend
- Strict rules about how many polling places per X many people
- Preferential Representation voting system instead of first-past-the-vote.
Look at how Australia does it.
For the remaining stuff, you need federal bills passed, so we're talking about both chambers of Congress + president. So the one party that isn't opposed to all that needs to have a trifecta, for starters. Majorities are razor thin these days, especially so in the Senate, so filibuster in the latter is another hurdle (although it could be dropped for something like this).
That's why it's such a nasty deadlock - the system is in a state wherein there are no legitimate methods to recover its operation.