chesswood – From my reading of the Act and my reading of the process you may not need a surveyor.
If you are confident of your claim that the tree is on the boundary and that the fence has been built around the tree and you provide photographs of the tree and the fence, plans of your Lot, etc then that will possibly be enough for your OC to bring a claim against your neighbour. During the Court deliberation process you will probably get a site visit to confirm the location of the tree and the boundary.
If your OC has done everything that it can to mediate this issue with no satisfactory result then you don’t need to contact your neighbours again. Your OC does not need anything else from your neighbour to bring a claim against your neighbour in the Court – their refusal to deal with you is sufficient to prove that they are being unreasonable and unresponsive. The mediated outcome has clearly not worked so another course of action is needed.
Just go straight to the Dispute Resolution offered by the Land and Environment Court using the information that I have outlined in my previous comment. Include as much information as you can to back up your claim including: photos; original survey plans of the Lot; timelines of actions taken including letters sent etc. Your strata manager may be able to assist. You may need to obtain the original plans from Council if your OC does not have them on record.
If the neighbours are to bear all or some of the cost of the tree removal then the Courts will make an Order to that effect. That should be the end of the matter.