Political parties at the municipal level are really bad in the US. I remember working under this highly ambitious person in college and I always got the feeling she was willing to throw us under the bus because we were really just a stepping stone for her to get somewhere "better". I imagine that when you sign up for a political party at a municipal level, you're already kind of signing away your decisions to whatever is most likely to impress the people higher up in the party. On the other side of things, people tend not to pay very much attention to municipal politics because it's very low-level and dry, which means that municipal people have a huge amount of power with limited oversight. That might be an exaggeration but it's kind of how I see it.
I like the idea of building credibility through solving problems. This stuff always reminds me of the Godfather movies: you would think it would be really hard for a bunch of violent, power hungry gangsters to get any sort of legitimacy in their communities but most of the time these groups are just taking advantage of holes in governance and solving problems and disputes the government is incapable of. Obviously taking inspiration from the mob is a... questionable idea, but I think that whereas people are very suspicious of experimental systems, nobody is going to argue with good food or clean streets or even something for their kids to do that keeps them from joining a street gang.
Homeless people are a good population to start with in my opinion precisely because they are so deeply disenfranchised and giving them a sense of purpose and community and something to be invested in could motivate a lot of them to try out experimental new ideas and spend a lot of time dedicated to solving the really tough problems in their communities. If the system can work for them and their very immediate problems, it might be easier to convince others it would work for them.