This is why legal "advice" on the Internet is so problematic. It's true, it's not illegal under most circumstances to screw someone in a business deal (which is what renting is). However, you can still sue someone for damages caused by an action that is legal. For instance, if the OP has to stay in a hotel and pay for storage, that might be something you could recover in court. Or, in some cases you can sue for "specific performance," which is a fancy way of saying that the court forces the defendant to do what they said they were going to do. Not a good idea, in my humble, personal opinion, to pursue that in this case because it's rarely wise to have a landlord that hates you and is only renting to you because of a court order.
"Made whole" is not just getting back your deposit. It also takes into account the fact that you have "relied" on the other party fulfilling their end of the bargain. The thing is, hiring a lawyer to sue is really expensive. The OP can probably rent a storage unit for a month, stay in a hotel for a few weeks, and find a new place. That's only a few thousand dollars at most. And then even if you win you have to collect, which isn't easy or necessarily possible depending on the resources of the person you're trying to collect from.
I'm not a lawyer, and nothing I say is legal advice, but I would, if it were me, get a firm quote from a storage facility and hotel in the area for a month's storage. Send a registered letter to the landlord and let them know you will accept a cashier's check for that amount in lieu of moving in according to the contract. There are tricky legal issues in threatening to sue without actually doing so.