It was an overflowing crowd for a district overflowing with problems.

The three top candidates in the race for San Francisco District Six supervisor gathered Tuesday night at the offices of Cloudflare in the heart of San Francisco’s tech-rich South of Market to stake out their positions on the problems and possibilities of the city’s busiest and most challenging neighborhood, an area that includes South of Market, the Tenderloin and Mission Bay.

The race to succeed Supervisor Jane Kim features school board member Matt Haney, housing activist Sonja Trauss, and former Planning Commissioner Christine Johnson.

Even more than the mayoral election that just narrowly put London Breed in the mayor’s office, the race to be decided in the November election is shaping up to be litmus test of many of the city’s most pressing problems: homelessness, crime, dirty streets and the housing affordability crisis.

That’s because District Six is home to the most of the city’s billion-dollar tech companies and its tallest new residential towers. It has the largest homeless population, the highest crime rate and the most congested streets. More than 60 percent of the new housing constructed in the past decade has been in South of Market.

During the debate, moderated by former Chronicle columnist C.W. Nevius, the differences between the candidates were more about style and priorities than stances on issues. All three said they support Proposition 10, a state ballot measure that would repeal Costa-Hawkins, the law that limits rent control to buildings constructed before 1985 and allows local governments to reject it altogether. All said they support the late Mayor Ed Lee’s goal of building 5,000 new housing units a year. All said they were for safe injection sites.

But the approach to how to meet these objections varied.

Haney portrayed himself as nonideological and solutions-oriented and said he would focus on the on street issues. Trauss, who has built a national movement out of the simple idea that popular urban areas should “legalize housing” to prevent displacement, said that she would work to force neighborhoods across the city to accept affordable, multifamily development. Johnson, an engineer with deep knowledge of public policy and 14 years experience in public finance, said she would bring to the job clear understanding of what she wants to achieve and how to do it.

Trauss and Haney took the most shots at each other.

Haney questioned Trauss’ focus on building housing outside of District Six — her nonprofit, YIMBY Action, pursues a “sue the suburbs” campaign that forces communities outside of San Francisco to build affordable housing. Trauss said the only way to solve the housing crisis is to force every neighborhood in the city, including the development-adverse west side, to accept more units.

“Four years ago when I started organizing renters, the city controller said we needed 100,000 units — he said that as a joke number that obviously it wasn’t something we could do,” Trauss said. “What I said — what the YIMBYs said — was ‘why not? Let’s do it.’ Now it’s so much a part of the conversation that both my opponents are running on a pro-housing platform.”

Haney said he would stick to District Six.

“I am not running to sue the suburbs. I am not going to pick fights on the other side of the city. I’m not going to shout people down on the steps of City Hall. I’m actually going to fight for you all, the residents of District Six,” he said.

All three candidates bemoaned the conditions on the streets of District Six. Trauss said she “wanted to be able to walk down the street with my kid without worrying about him picking up a needle.”

Johnson emphasized her working-class roots in New York City where her mother, a nurse, worked two jobs but was still unable to keep up with rent.

“Every two years, we would get a rent increase and have to move,” Johnson said. “I had eight different home addresses growing up and I decided early on that I wanted to dedicate my life and my career to making cities a place where everyone could live life.”

She said as a planning commissioner she had helped create child care facilities, worked for transit improvements and approved more than 10,000 units of housing. But she said she realized that none of those efforts matter much if the city is unlivable.

“I realized that nobody is going to care about any of that if you are stepping over poop and needles and you feel like you can’t stay here because housing is unaffordable and you can’t make a life here,” Johnson said.

Haney, who has been endorsed by incumbent Kim, said the district has been too often ignored by the city establishment.

“We are not getting the resources we need,” he said. “We have been failed by City Hall. We have been failed by the Planning Department. Our residents need a champion, someone who is focused here, block by block.”

J.K. Dineen is a San Francisco Chronicle staff writer. Email: jdineen@sfchronicle.com Twitter: @sfjkdineen