I've spent over an hour looking at the log files you sent and then experimenting to see if I could make a similar thing happen for me. Unfortunately I can't replicate the problem at all.
The logs describe a situation which doesn't make sense; they show you successfully sending some 4500 books in batches of about 700. Then, on your next connection, when CC and Calibre exchange information their respective libraries, Calibre states that it does not recognise any of the books in CC. This is baffling, as it's stating it doesn't recognise the books that it sent over itself. The connection process then fails shortly after this step.
Ticking off potential causes: You're using a recent version of Calibre, and we know the problem is unlikely to be in Calibre's side because otherwise this forum would be full of messages. However, at the same time no one else is reporting an issue with CC's wireless device connection.
It's true we previously had issues with a crash when synchronising large libraries in the iOS version, but that crash happened at the start of the connection process, when CC was getting ready to send its information to Calibre. That's definitely not the problem here since both sides' logs show the transfer of metadata regarding the 4772 books. So it's not that either.
I don't know where else to look. I've tried sending text files (rather than normal book formats), I've tried increasing my test library size, and nothing breaks it for me.
I think we just have to go back to that offer of a refund.