Hi Flutterby,
I have had some trouble withSIJ and lumbar spine too. One thing that really helped the SIJ was this simple youtube clip:
YouTube - SI Joint Treatment
Give it a go and see if it helps. In terms of hard research, there is no evidence to support the SIJ being out of alignment because the movement in SIJ is very very minimal. That doesn't mean that it can't be a source of symptoms or that it doesn't respond to manipulation/mobilisation. But yeah this just means that the SIJ is not really understood.
This is also a good video about muscle imbalances:
YouTube - Muscle Imbalances