I've heard great things about Matrix. Peeble's founder, Eric, was building Beeper, a chat app with a similar purpose to what you describe (it recently got acquired by Wordpress). I believe that the core was built on top of Matrix, so you might be up to something there.
Building auth stacks is not trivial and is not what will make your SaaS successful. The more you can leverage experts to focus on what makes your SaaS special, the better.
Coffee shops are better for a weekday. There might be troubles with wifi reliability or power outlets(there might not be), noise levels, people walking all the time. I found out that I prefer to go to cafe Reveille. It's nice and clean and they have pretty decent wifi, though they don't have any electric outlets. Another option is a Starbucks on Fillmore street. Main benefit being that it works until 9pm almost every day, and you can crank up few solid hours there after work
The main library (the one by the Civic Center) closes way later than the rest. Good spot if you're working alone.
This sort of "just" thinking is a great way for teams to drown in ops toil.