Fortunately I managed to find a combination that worked for me. The most important component was using a break program that made sure I took breaks to rest my arms and hands, and to do some exercises. I also switched to an ergonomic keyboard and mouse. I am now completely recovered, but it really made me realize that we need to pay attention to ergonomics.
I've written up my story in more detail here: http://henrikwarne.com/2012/02/18/how-i-beat-rsi/
In addition to what I mention in my post, I am now also using a height-adjustable desk (some people think they are expensive, but they're not). It's really good to be able to switch between sitting and standing. If you are like me for the first 10 years of my career (i.e. ignoring ergonomics), consider paying a little bit of attention now, otherwise it may become a problem later on.