Mark, I would guess the Twentieth Century Limited, but part of its route ot of NYC/GCS was powered by "shoe" and the route is more than 500 miles long.
We know that the train used what are today called "slab-sided" coaches as opposed to fluted or streamlined ones, that its route was less than 500 miles, no part of its run was electrified, that one of the terminals was Chicago but the other one was not Detroit. Also that at least some of its run was over the old New York Central.
I'm a loss. The only clarification I can think of this time is to ask whether this train, at any point in its history as a passenger train, carried "slumbercoaches" (aka sleepercoaches -- no need to be picky about the brand name). - al