This reminds me of a third option that I'm surprised I didn't think of earlier: the Alexander Technique. Tension arising in the neck and upper back areas is practically their specialty. I got some amazing results working with a good Alexander teacher.
Incidentally, if your situation is anything like mine (and of course I don't know), you may need to make some changes in your life in order for the pain to go away. I'm not talking about techniques, I mean fundamental personal change. I had a headache for 9 years. No one ever explained it. But it eventually went away as I addressed some important issues in my life.
Not being able to take a break for hours at a time means that if your RSI continues getting worse, you will not be able to work there anymore. The RSI stuff I have read has suggested breaks every 20-45 minutes in order to not make things rapidly worse and end one's career.
I'm most definitely not a doctor, of course, but your body is already overly stressed and breaking down. It needs more time to recover, at the very least.
The hand/arm stretches help but only up to a point. A lot of the tension I get seems to arise in the neck and upper back areas. I feel great when I get out of the gym or after a hot bath but I work in a pretty high pressure environment where I sometimes can't take breaks for hours at a time. Maybe that's the real problem. But I was hoping for a workaround.