So, I make the jump onto the train the first try, start driving down and looking for the engine, and after a few seconds I think, "Well, that looks like it, but why is it coming towards me?" Suddenly I'm knocked off the train, mission failed.
Restart the checkpoint, try it again, and then I get a better look: apparently Rockstar forgot to code into this mission that there shouldn't be any other trains on the tracks, because there was another train going THROUGH the mission train, in the opposite direction, and I was getting knocked off by the engine of the train ghosting through the train I was driving on.
Was beginning to worry I was going to have to quit the mission, because every time I restarted the checkpoint, it happened again. But after a few times, I guess the other train had finally passed, and I was finally able to get to the end of the train sequence... where it had a head-on collision with another train.