I'm still of the view that an application to vary the orders is your best option, here.
In contravention proceedings, the Court has jurisdiction to amend primary parenting orders, and it has jurisdiction to grant leave so the parents can apply to amend primary parenting orders in the course of contravention proceedings, but it also has many other options, too, many of which are probably going to be more attractive to the Court than amending the primary orders in favour of equal care. For example, if all mum did was change the child's school without your consent, the Court will probably make an order for which school the child attends and order mum to enter into a bond. Or it might grant mum sole parental responsibility for education matters. Or it might order you both to attend a post-separation parenting course, or mediation to discuss the child's schooling options.
But a contravention application does not guarantee the Court will consider varying the primary parenting orders to what you're seeking. It's an option for the Court to consider, but not one that it is at all obliged to follow, and in my experience, it's not one the Court does follow in the magnitude that you're suggesting (ie going from orders for every other weekend to equal time just because there was no agreement on the change of schools).
Before the Court even gets to considering what outcome is appropriate in the contravention matter, it first needs to be satisfied that a contravention has occurred without reasonable excuse, and frankly, that's not a walk in the park, especially around matters of parental responsibility. Parental responsibility requires a genuine effort to reach agreement jointly about major long-term decisions affecting the child, so just because there hasn't been agreement, doesn't mean they haven't met their obligations of shared parental responsibility.
The Rice & Asplund threshold for a variance, however, is probably more attainable than proving a contravention without reasonable excuse in your case, because the orders are so old, both parents have moved and both parents have agreed to different care arrangements anyway. Mum would have to raise a Rice & Asplund argument against the application to even invoke the threshold test, and she may not do that anyway, given how vastly different the circumstances are now since the orders were first made.
If it were me - and I'm just a stranger on the internet, remember, but if it were me - I would attend mediation and try and negotiate agreement by way of parenting plan that when you move to where mum is, you see the child more often. If she doesn't agree to any variance, then move to where mum is, and file your initiating application as soon as possible thereafter.
The suggestion to seek equal care before moving just seems obscure, to me - why would the Court consider equal care when you're still living 200km from the child and the child's school, just the same as you were nine years ago?
I think you would benefit from legal advice, because I think the various opinions here may lead to more confusion than assistance. Legal Aid does offer three free consultations per family law matter. It would be worth sitting down with them just to decide what your best course of action is, even if you intend on representing yourself.