Solution
It is impossible to remove the built-in Thunderbolt 3 MXIe controller from the PXIe-1083 chassis and replace it with the PXIe-8361 remote control module. The PXIe-1083 lacks PXIe controller connectors on the backplane, meaning a PXIe controller will not physically fit. While there are backplane connectors for the Thunderbolt interface, these do not accommodate standard PXIe controllers.