ASERNIP-S has not conducted a review on sympathectomy. It was previously listed for MSAC to review (hence why ASERNIP-S did not review) however I believe instead it was referred to PBAC. I have no information as to what happened with this review although I recently found out that it was only looking at a pharmaceutical treatment. ASERNIP-S is only able to review the published evidence however our current funding does not cover conducting any new systematic reviews. We would be happy to do a full systematic review on this topic but this would require significant funding, in the order of $150,000. The reason for this is that we would need to examine all study types in detail, as it is clear from what you have provided there is an enormous evidence base.
All that I can suggest is for you to contact the federal government, possibly MSAC and state governments for funding to have a full review done.
In our searches we located a guideline paper on the procedure from 2007 which indicates that the procedure should only be considered in severe cases when alternative treatments have been tried and were unsuccessful.