I'm so sorry to hear about your dad.
I am wondering the same about wait times, for different reasons.
Does your child have dual citizenship? If so one thing I considered when we couldn't get an embassy appointment: fly back in half term when people are still allowed to enter on expired passports (through March), renew child's passport while in the US using my parents' address (they live in a small town that has loads of appointments available), child flies back on the UK passport, parents fed-ex the passport back to the UK for us when it's ready. I imagine you don't want to burden your parents with that. But it might be an option if you're desperate or plan to be in the US for a few weeks?!
Good luck with everything!