Storage Company wants rent+late fees, AND locked me out. Not yet Executor, I can't pay. How do I not lose Dad's things?

Dad died on the 13th of May. At month's start, he'd always auto-paid his storage (for flea market stuff he sold) rental fee --nearly $400-- with one credit card he had just for that purpose After Social Security was notified of his death, that credit card company closed that account, so the storage hasn't been paid. (I'd told them later in May that he'd died, I was named executrix, but we all had to wait for the probate process before I could access any of his money to pay any of his debts, hoping they'd understand.) A week into June they called and told me that rent was late+there's a 20% late fee on top of it. (His other storage costs less than $80, and had another space open.) Maybe a week later, I went to get his stuff out & over to the new storage, but when I got there, I found I was locked out. Don't things "freeze" as of Date of Death, so creditors can't charge late fees? Do I have any recourse? I'm still grieving, now feel "screwed over" by them as well.