To begin with, I'm very sorry to hear of your loss.
I'm a bit late getting into the discussion, but have a few thoughts to add.
It would help if you could clarify your criteria of "decent accommodations". Are you looking for a hotel, Air BnB or other types? Sorrento has a good range of hotels and it's hard to believe that they're all sold out in mid-September. Perhaps they aren't booking for September yet?
You could also check out your local library or book stores and have a look at the current Rick Steves Italy guidebook. The accommodations listed there are all checked by Rick or his staff, so they're reliable. The guidebook also has information on local car services, trains, ferries, etc. The books are also available in Kindle or Apple Books format. I've found that having that information at hand makes the planning a lot easier.
As previous replies suggested, you could also check other towns along the Amalfi Coast. Positano might be a bit problematic as transportation there can be a bit challenging at times. Salerno is another possibility. Check the Trenitalia website for information on trains in the area or this website - https://www.campaniaexpress.it/?locale=en .
That's all that comes to mind at the moment. If I think of anything else, I'll post again.