I've mulled this over, and the best bet for both would probably be for Amtrak to simply pull a set of through cars off their LD trains and hitch them to an FEC corridor train, either "renting" a pull from the FEC or paying them a percentage on the run (or however operations like this were done "back in the day"...for example, how was the division done on the California Zephyr?). Note that Amtrak expects adding the service to be a net boost to revenue, so there's probably room to negotiate.
Ever heard the expression, "Borrowing Trouble?"
That sounds like much of what you are doing here. "Back in the day" there were multipe examples of through running of power, diners, and everything else. An outstanding example would be the Chicago to Florida fast three, City of Miami, South Wind, Dixie Flagler, which after the Dixie Flagler was discontinued became the fast two. These trains all operated on the FEC in Florida where they were turned over to the ACL. At Waycross they went three different ways with no other common point, even to each operating out of a different station in Chicago. (The South Wind and Dixie Flagler both went through Nashville, using the same station, but using different routes into and out of the city. The South Wind and Dixie Flager both went through Birmingham but stopped at different stations.) After through cars to Tampa and to St. Petersburg became part of the mix, equipment to these points became part of sections of the West Coast Champions (Bill Haithcoat, tell me if I am wrong here) to those points. In addition to the Forida East Coast and the Atlantic Coast Line, railroads involved were the AB&C (later to be part of the ACL), the NC&St.L (later to be part of the L&N), the L&N on two different routes, C&EI, Pennsylvania, Illinois Central, and Central of Georgia. Should not forget the C&WI in approach to Dearborn Station. Also, there were such other things as the Illinois Central trackage rights over the GM&O, Southern, and Frisco between Jackson TN and Birmingham, the L&N use of the Southern Railway bridge at Decatur AL, and probably some other odds and ends I have either forgotten or never knew.
Saying all this to say that arrangments involving multipe railroads in operation of trains of any and all types has a really long and convuluted history.