Breaking a Lease: Are Early Termination Fees Part of the Lease Term

My question involves landlord-tenant law in the State of: Washington

We have broken a lease in accordance with the terms of the contract (i.e. correct notice period in the correct format) and our contract states that the the "tenant shall pay up to 1 months rent for early termination fees, with a minimum fee of $400", basically the actual value being dependent on when the landlord found a new tenant to move into the apartment.

Our problem is that the landlord is stating two things with regards this:-
1) That we remain responsible for maintenance of the apartment even after we have vacated it and our termination date has passed.
2) That we have to pay the termination fee now, even before we have vacated the apartment and our lease has terminated.

Think its better if I give an example! We give notice on 5th September for vacation/termination of the lease on 30 September (all in accordance with the lease). Assuming our landlord does not find a tenant to move in on 1 October, our landlord is stating that we are also responsible for maintenance of the apartment in October . This does not seem correct to me as our termination date would appear to be 30 September and as long as we pay the termnation fee when we move out on 30 September all obligations for the apartment would seem to cease on that date.

Additionally paying the termination fee on the date we move out (i.e. 30th September) as opposed to when the landlord is demanding it (i.e. now...7th August) would also seem more appropriate. Please note the contract is silent on when the termination fee should be paid.

Be grateful for any insight.