Last I read, Both Freedom of Expression and the 13th Amendment are applicable. He has the right under the 1st to express his religion and Hobby Lobby confirms it applies to his type of business. As far as forcing him to labor for another against his will, with no contract for specific performance it would violate the 13th. It involves personal labor not just the selling of a fungible good.
I mean there are so many arguments to use to defend. I hope their attorneys use them all, correctly, and well.
THEN ... it can be appealed on Constitutional grounds, if it is as you say ... and they will win (again, given that your stated understanding here is correct).