$400?! Good for you, but sorry about the heat! When I searched for hotel rooms the cheapest I found was $2000. Er...I didn’t go.
They might have been full too, but another option is staying at one of hotels near BWI (Baltimore) airport. Most have a free shuttle to the train station. Fare is $8 to Union Station on some trains and if you have a Medicare card it’s $4. Amtrak is like $30.