Influencing CDN traffic

I run a small ISP network in Australia, we have various transit and peering arrangements. I have bilateral IX peering with Akamai in the two nearest cities (Melbourne and Sydney), Yet some %75 of the traffic coming from their AS still comes in over transit. I took this to mean that traffic is coming from a different geographic region, where transit is the most cost effective path for Akamai to reach my network - So initially my thoughts were around identifying the source prefixes, then trying to geographically locate them so I can determine what locations might provide beneficial peering arrangements.

It has occurred to me that I don't really know how a CDN works and I might be approaching this from the wrong angle. CDN data is distributed across the globe, and logically at some point in the connection there must be a decision made as to which server to source the data from. How is this decision made? I found this 6 year old presentation talking about Akamai using some proprietary 'mapping system' - https://www.menog.org/presentations/menog-14/282-20140331_MENOG_BGP_and_Traffic_Engineering_with_Akamai.pdf - and while it's quite comprehensive it doesn't really tell me how to influence that mapping.

I've identified that there are two specific prefixes that the bulk of this transit traffic is coming from, and they both appear to be only advertised from Akamai into a telco's AS (Telstra) and then learned by the global internet from there. Is there some sort of monopoly on these CDN locations, do Telstra pay Akamai for the privilege to host a CDN in order to improve their SP network offering? I understand from that earlier linked presentation that Akamai's CDN is 'non-network' meaning there's no private backbone between their servers, but surely it would still be in Akamai's interest to advertise those local prefixes into every local IX at least and perhaps even publicly share that information.

Am I way off the mark here? Is there a way I can influence selection towards servers that are accessible over my peering arrangements?