Responsibility To Pay A Dead Parent's Assisted Living Bills?

My dad died a few months ago after battling cancer for several months, the last of which required him to move into assisted living. He wrote his last check to the facility on the first of the month; later that same day, he went to the ER, where it was quickly found out that he had very little time left because of a complication. Within a week he entered hospice, and signed a legal document to step down of the trustee of his various trusts, and I signed documents accepting that role instead. I hustled to clean out his apartment as soon as possible so we could get a refund for the balance of the month, which his resident manual said we'd be owed as soon as the apartment was broom clean. He died just a week later, and I became the executor of his estate as well.

When I emailed assisted living after his death, though, they said that the check dad wrote before his death was invalid, apparently because they'd waited to cash it until after he'd stepped down as trustee, and maybe even until after he died. They claimed I now owe a pro-rated amount for the first 10 days of the month, between the original check was written and when I cleaned out the apartment. I countered that I'd like to see a revised invoice reflecting a credit for the meals he didn't eat/care he didn't get that month, because their handbook says they're required to do that.

But now I'm wondering: do I actually have to pay at all? My dad's estate has no assets subject to probate and everything was held in trusts. I didn't personally guarantee that I would pay his bills to assisted living in the event of his incapacity or death, though I had PoA. Our state gives creditors a six month period to make their claims, and I'm sitting on enough money to pay the bill; a couple of the beneficiaries, though, are anxious to get the full amount of their inheritance, or at least know what number to expect. I have an estate lawyer but I have a feeling this is a simple question and would love to avoid another micro-bill for emailing them, lol.

Location: Missouri.