landlord withholding part of security deposit — no move-in checklist

I’m currently in the midst of a dispute with my former landlord over a few hundred dollars withheld from my security deposit. Despite my best efforts to clean the place, they’ve claimed that several hundred dollars were needed to professionally clean the apartment. However, no move-in checklist was ever drafted or signed upon move-in. When I saw the money taken out of the deposit, I emailed them mentioning this and cited the appropriate laws, and asked that they return the rest to me. They emailed back doubling down on the reasons why the deductions was necessary, but acknowledged they did not have a move-in checklist.

I’m thinking to ask them one more time politely and then notify them that I’ll take them to small claims court if they don’t return the money. Is there anything I’m missing here? The law seems pretty airtight, so I’m hesitant to squabble over the details of whether or not the apartment was left up to par. (e.g. if I blew up a stick of dynamite in the oven, would they still have to return the entire security deposit to me?) Also, how would one go about proving that a move-in checklist never existed—is that on the landlord? Just want to make sure I’m 100% in the right here. https://www.seattle.gov/sdci/codes/common-code-questions/deposit-returns

Thanks!

EDIT: for reference, they did provide an itemized invoice of what they charged for. Just no move-in checklist.