I was involved in the initial development of the Engineering option (Tunnels) in Survey Controller and later the Tunnels apps in Trimble Access. I'm pretty sure the TXL files used by Survey Controller didn't use surfaces in their tunnel templates (called Tunnel shapes in TBC). Because of this no TXL created or used by the current versions of Trimble Access or or any version of TBC will not be compatible with Survey Controller (which was discontinued about 12 years ago). This means to continue using Survey Controller you will need to recreate the TXL file in Survey Controller.
The S6 total station is still supported by the latest version of Trimble Access. Instead of continuing to use your TCU, you might be better using your S6 with a controller running Trimble Access.