Ok so you're not gonna like my answer, so I'll be blunt in writing it...
If CSA rules meant dad was responsible for stuff above Child Support according to their rules, don't you think CS would have the capacity to collect that $$$ on your behalf? of course... But they can't / dont? WHY? because their rules don't say that dad has to pay...
Here is a link to their rules
Using the Child Support Guide | Child Support Guide
It will send you bonkers reading it, especially because what you're looking for doesn't exist.
With respect, you cant force dad to pay beyond childsupport. So you're picking a fight you can't win. Back in the day, I worked on a principle that I would pay extra to keep things sweet between me and the ex. Sadly, my ex took advantage of this and just kept hitting me up for more $$$ and in return told me the extra was not good enough... Now I'm not saying this is what you've done... Just giving you a different perspective. The end result, I paid child support because that is exactly what I was assessed to pay... Now again, I did warn you that you were not gonna like my answer... I found it very frustrating that my ex would be very quick to tell me that I was only paying the minimum... A whole lot of guilt tripping... It got me thinking... so if i go shopping and when I get to the check out, I'm told the total is $55. Would I choose to pay $60 because I don't want to pay the minimum?
So my suggestion... Ask dad if he would be prepared to pay 35% of stuff since he has 35% care. But the reality is he does not have any obligation (according to the rules) to pay.
The best I can find is this example from the child support guide... So in this example CSA would not increase child support in an example where a kid was going to a private school.
2.6.9 Reason 3 - High Costs of Caring for, Educating or Training the Child in the Manner Expected by the Parents | Child Support Guide
When is the cost of maintaining the child significantly affected?
Once the costs associated with educating, maintaining or training a child in the manner expected by the parents have been calculated, the Registrar will consider whether the additional amount is significant in relation to the assessed costs of the child. If the additional amount is small in comparison with the assessed costs, the Registrar may find that the costs of maintaining the child are not significantly affected and that there is no reason to change the assessment (section 117(2)(b)(ii)).
Example: Royle and Misty have agreed to send Annie to a private school. The cost of Annie's attendance is only slightly higher than it would cost for Annie to attend a government school, and the additional amount is only a small proportion of Annie's existing assessed costs. The Registrar finds that the costs of maintaining Annie are not significantly affected by the costs of educating Annie in the manner intended by the parents.
So when can dad be expected to pay extra?
2.6.8 Reason 2 - the Special Needs of the Child | Child Support Guide
Ok so the kid needs braces? cost $15 000. Dad could be grounds for csa to collect... But even then according to their example in the link it states "may be significant enough" So no guarantees on that one...
Now with respect to the person you spoke to on the phone. God bless them.. I can't think of a worse job... But they are not well trained and it is stressful. They use the same guide I have provided to you. They are often rushed and in my experience often express their own opinions as facts. That is a huge part of the reason I chose to learn their rules myself rather than rely upon someone at the end of the phone who has had a few days training.
Like I said, feel free to read through the guide it will send you bonkers, so you can understand why their front line phone workers get it wrong... But you will not find anything anywhere that tells you that dad has to pay for anything beyond the assessed child support amount...
U'm, final thing... My ex, back in the day, she would give me reciepts for stuff like sun-screen, movies (popcorn and all), coffee bought when hanging with her mothers group mates... So while I'm sure you're not gonna like my answer, I hope you can see my perspective in the way I've written it and I hope you can understand that I'm pretty confident that i am right on this one...