So, firstly good work in getting a reply. That means you’re sending the right people, the right message.
With specific case, I would play into their obviously inflated ego and also lean into the curiosity loop.
It sounds like you’ve got a great system in place.
I might not be able to help, but I have worked with a client similar to how you’re set up.
We made a couple of subtle changes that had a decent impact.
Would it be worth a quick 10 minute call to see if you’re already implementing them?