It really would be as simple as a short extension southward, and setting up a class system for train dispatch. NASA and USAF trains would run as first class with an absolute no interference policy, the port trains would run as second class, inferior to all first class trains. It's an easy fix if they can pull it off, but it will still require 10+ miles of track and a 3-4 mile bridge and causeway or a longer route past the VAB and south through Cape Canaveral AFB.
Simple, but not easy, that is still Cape Canaveral Air Force Station and it is not easy to get on that facility, still to this day. The rail lines you speak of have closed gates on both sides of the road, basically saying, go away. Sure it CAN be done, but this will not happen without a decommissioning of the NASA area or CCAFS going away all together from this location.
The CC docks are paltry compared to Miami, Jax, Tampa, FTL, the state is setting up its best candidates to serve cargo, why go to the expense to add yet another candidate? Why add all this, when the docks are already thriving with 2-3 cruise ships each week? That is their bread and butter our of Port Canaveral, not containers.