You just need to add a third rule to the Cross-Docking Route.

The rule would monitor the arrival of products into the Stock location and create an Internal Transfer to move them to the OUTPUT location.

The existing PUSH rule which creates Delivery Orders when products arrive in OUTPUT would then kick in and create the Delivery Transfer for you.

Transfers created with this configuration, assuming you change the destination location of the INPUT --> OUTPUT Transfer to STOCK instead (when your cross-dock is full):