Randomly drawing citizen. Sure politics require some training, but it can be done on the job

Also, countries with proportional votes tend to force politicians to talk with each other more than countries with single representative per district.

Limiting elected official mandates to one or two. If you couldn't do something in 10 years no reason to think you'll do it latter

Well my good-faith arguments would be direct democracy (i.e. everyone votes on every change) or ranked choice, but that has its own problems. However, you didn't say it has to be serious. So I suggest a system that locks a chimpanzee on LSD into a room with signs (options) and blinking lights. Chimp starts rolling and points to the blinky light he likes (or hates) either way, your government is operating far more efficiently than hairless apes doing something that is apparently too much work, and most are just as ill-informed as acid-chimp. I honestly think acid chimp accidentally gives you a better (albeit random) set of values than capitalism/democracy ever has.

A bit is specific, but you can probably adapt them.

1. Bring back pork spending, it's over all cheaper to spend 100 million on some garbage than beating people into submission to pass something.
2. Increase number of representatives significantly, makes some things less efficient, but also massively reduces the power of lobbying, and increases the power of localized activism.
3. Limit length of allowed legislation per vote. Smaller more focused bills are ultimately better than sweeping legislation that attempts to address everything. More votes also makes working together easier with lower stakes and more opportunities to collaborate.

Soviet Democracy. Workers elect delegates from among themselves, who can then be subject to instant recall elections at any time. Remove the "career politician" aspects from government.

End FPTP. House of representatives actually representing the people instead of state or party. Senate still representing states but not parties.

A bicameral legislature, one house elected by mixed member proportional system and the other selected at random from the voting age population. Legislation must pass both houses, if it passed one house but not the other it can go to referendum at the same time as the next general election.

You can also have things like citizen initiated referenda. Campaign finance laws similar to those in the UK are also desirable.

Greatly expand congress (like at least 10x), and have it work like jury duty.

What's the opposite of congress?

Progress

IMO anything with a direct vote of the people will end up as spending wars between special interests with the funds to advertise.

We all upvote or downvote a law

Everyone forms communes that reflect their personal values. I would prefer one with direct democracy, and no representatives.

However big a commune you want, but I'd recommend keeping it at 2000 people or less. Anymore and people start to see each other as strangers, not community members. Plus direct democracy works better with smaller population numbers.

Define a set of rules, and someone will figure out how to cheat it.

I don't see the problem originating from Congress necessarily being polarized. I think the problem is that corporate and big money interests are too strong, and they fund politicians that will try to divide the people on social issues so that they can distract the people from badness happening on the economic front. In other words, I think we're seeing a problem with corruption that's expressing itself as polarization.

Even the term "polarization" can also be used as a trap, because it tends to be used in a way that frames politics as a linear spectrum, and your views are somewhere between these two end points. In reality everything is far more complicated. People have highly nuanced views on many different subjects with good reason, and there's no way you can easily capture it on one single sliding scale.

There's a few ways in practice.

1. Court decisions are binding broadly. The conservative capture of the Supreme Court is political genius, honestly. They tend to have the final say regarding policy.

2. Federal agency rules are also broadly binding. EPA rules that limit greenhouse gas emissions, for example, apply everywhere in the country.

3. State legislatures are often less polarized, which facilitates a more productive legislature.

4. State agencies, like a state environmental department, mirrors its federal counterpart but is more localized.

5. Non-state organizations can get things done, though their interests are often limited and not necessarily in the interests of the broad public as state and federal institutions are.

6. International institutions can 'set the tone'. They may not have any power to actually do anything within a specific jurisdiction, but people within those jurisdictions can draw policy inspiration from international organizations and try for something locally binding.

This isn't an ideal solution, but a practical one. A simple hack for the U.S. would be to make congressional votes secret. Yes, this means congress people would be less accountable, but think about where their accountabilites lie. These people are far more worried about their parties' strongmen and sponsors than their gerrymandered constituents.

Impossible to implement in the present U.S. climate, but more idealistic is to divide the US into 50,000 person districts (greatly expanding an individuals access to their rep), then group those into evenly sized super districts. The reps choose from among themselves a super rep to attend congress, who they can recall at anytime. This should make gerrymandering more difficult, and dilute the effectiveness of corporate donors while increasing the influence of individual voters.

I honestly wonder if sortition is actually the answer.