Unfortunately he followed the law. The Railway Labor Act of 1926 prevents railroad workers from striking. They instead have to follow the exact process that was followed and continue working while in negotiation. As a rail worker, to go on strike is to quit your job.
Edit: After rereading, the RLA 1926 will allow for “self-help” remedies after a minimum of 60 days have elapsed from the time the National Mediation Board begins it’s process. This allows 30 days of NMB mediation, followed by 30 days for a Presidential Emergency Board investigation, either of which can be extended and with the caveat that
The NMB can keep the parties in mediation indefinitely, so long as it feels there is a reasonable prospect for settlement.