What are the legitimate Islamic controls for charging the tenant the costs, or a portion of the costs, of maintaining certain things in the rented house, even if he was not the cause of the damage, or did not expect to continue renting for the period in which what was repaired would be consumed?

It is not permissible to burden the tenant with the costs of maintaining the leased property, because that leads to an unknown rent and invalidates the lease by agreement of all the madhhabs (schools of thought). The expenses of maintaining the usufructuated property are borne by the owner of the property (the landlord). The landlord is obligated to maintain the leased property, including renovation and repairing what is broken or leaning, and making and plastering doors. As for operational maintenance costs and repairing what has been damaged due to usage, there is no harm in the tenant bearing them.