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Hello and welcome! My name is ***** ***** I will try my level best to help with your situation or get you to someone who can.
As a landlord myself for over 26 years, I would agree that the hourly charge and the amount of time they are claiming that they cleaned does sound extremely high unless the house was just completely filthy and almost unliveable..
So your recourse here is to file a small claims court suit against the landlord for breach of contract and force him to prove that the house was indeed in such a shape that the charges are justified. If he doesnt' have pictures of its condition and doesn't get the cleaning company employees to come to court to testify, then he will have a hard time proving that the costs are justified and it is very likely that the judge would engage in some "rough justice" and substantially reduce the cleaning costs.
But I agree with first sending the landlord a letter, certified mail, contesting the charges and end it with a statement that if you can't achieve a resolution, you will file suit and let the judge decide what is fair. Landlords hate to be dragged into court and that will "encourage" him to work out a settlement with you..