A relatively new method that may be of help is whole body vibration. These platforms send vibrations through your body, creating reflex muscle contractions of between 25-50 times per second. All these contractions release endorphins, just like exercise. These endorphins help manage the pain and make you feel better, reducing levels of stress hormones.
In general, this also helps with energy levels and can also make you feel better. One study showed much improvement for about 80% of the Fibromyalgia sufferers. Because most of the exercise positions are stationary, you won't see all the muscle soreness the next day that you might with normal exercise.
All these contractions also increase circulation, which should be of help since people with Fibro often don't exercise because it creates soreness. I have recently purchased one of these platforms for my exercise studio and believe that many people such as yourself can help manage this better with this method.