Landlord wants to terminate lease after water damage

My apartment in Chicago got water damage from a burst pipe (not my fault). Several rooms have wall damage that needs repair. My landlord says they need to redo ALL the floors at once "for efficiency" which means I have to move all my belongings out temporarily.

They're demanding I pay $3,500 for moving/storage costs, saying it's my responsibility. My renters insurance is covering temporary housing but not the moving fees (because the floor remodeling is largely cosmetic and not a result of water damage). I want to stay in the apartment and just deal with the necessary repairs, but they refuse. Not willing to compromise on doing things one room at a time etc.

Now they're threatening to terminate the lease under the damage clause (lease says it can be terminated if premises become 'uninhabitable') if we don't move our things quick enough.

Ultimately I think I'm out of luck with this large sudden expense. Just curious if other people have had the same experience or advice.