We have discussed this already over chat. We're going to give you feedback from Texas Instruments about the clarifications you need. We'll send you a message once we get a response.
We got a response from the manufacturer. They said that the connectors for the ControlCARD are these part numbers from Samtec:
I have also sent the ControlCARD dimensions to you. I hope this helps. Let me know if you have any further questions.