The stay posted on the account but I can't retrieve the folio.
Your meaning, I presume, is there is no folio attached on the Hyatt website to print out (as opposed to there is a folio attached but it will not open or download)?
I presume the hotel is neither close to your home, nor a recurring destination, so going back past the hotel is not an option? (Which I did once by rerouting a connection, but that was a more involved story with a bit of money involved).
Back to your situation. Some years ago I had something similar happen. I finally got the hotel to verbally give me the detail of charges over the phone and I typed up an explanation for my expense account. Boss initialed and it flew. The person processing the claim was far more concerned about having something, anything, in writing she could scan that added up than exactly what form the documentation was. Just maybe it would work for you, or is your accounting group way more buttoned down than that?
Paper is still your friend and hard copy receipts have saved me a few times. I also learned to not settle the bill till I left the hotel. But I realize when it is time to collect it there can be empty front desks and shuttles to transport about to leave and everything running late; so that does not always work out.
Hope it works out for you.