I've been struggling a lot with my back at work and my boss has allowed me to work half days in the office and half at home and it's really helping, not sure if that's an option for you x
I would highly recommend seeing a pelvic health physio. Try and get referred but if not I ended up paying privately with my first baby. I am also hyper mobile and ended up signed off work at 24 weeks first time round 😣 I'm now 20 weeks with my second and doing all the exercises I was given previously, things are soo much better. The good news is the pain completely went away after birth 🙌🏻
I also work in an office and sit the way you describe. I use a pregnancy ball part of the day and it helps a lot to take the pressure off my lower back and keeps me from getting into the spider poses.