Just wanted to update this thread in case anyone else happens to be searching for help with this annoying wrist issue in the future.
I'm happy to report that my tenosynovitis eventually cleared up after several months and various angles of attack. I ended up wearing a thumb splint to totally immobilise my thumb during the period of worst pain (2-3 months), both at day and night. In hindsight this was probably more helpful for my comfort than doing anything to help the healing. After about 3 months of attempting to manage it by myself I got fed up and went to see a physio and after 3 sessions of her massaging and doing ultra-sound and me doing daily massage and icing, it started to clear up. I reckon I've been free of the pain for a couple of months now and can pass Finkelstein's Test no bother. I've kept up the massaging, but now only do it about once a week, just to be safe.
I'm pretty sure it was the massage and icing (i.e. increasing blood flow to the injured area) that made the big difference, but I also had to change the movement patterns that caused the problem, in particular picking up my toddler ands especially getting him in/out of the car seat.
Fortunately, the injury never really affected my climbing and in the period that I was rocking my 'Mummy's Thumb' splint at playgroup I was scraping my way up some of the hardest and best boulder problems I've managed.
Anyway, hope this might help someone in the future.