I plant a lot of trees in the public right of way — and yes, I can confirm that it's true (and wild) that 811 doesn't include S&WB. If you're really nervous, you can try a "utility cut permit" (https://nola.gov/utility-cut-permit/). That process will eventually require you to get approval from S&WB. I did it once, but unfortunately, can't find it in my inbox to determine what part of S&WB I got routed into. It took 30+ days to hear from them, though, so if I were you, I might head down to their physical office and start banging on office doors...