USB-C Connector: How to route signals
I'm by no means an expert in this area so I'm not sure if this will help or not, but I happened across a message thread on an Autodesk forum titled "USB Type C super-speed routing doubts" that seems related to your question. The designer seems to be using the same MOLEX(?) connector as shown in your figure. Perhaps it has information that'll help?

https://forums.autodesk.com/t5/eagle-forum/usb-type-c-super-speed-routing-doubts/td-p/8219947

From what I can tell by reading the message thread, these designers are putting very small 0.3&nbsp;mm vias inside the 0.5&nbsp;mm gap between rows A and B (see message #39). See also messages #36 and #37 in the message thread.

And in case you're unaware, high density interconnect (HDI) boards frequently use laser-drilled microvias. Here's a couple good YouTube videos on microvias: 

https://youtu.be/rByRMd7JmTs

https://youtu.be/TI5FfG0JSes