Firstly, the CSR told you to go to the wrong place. It should have been the library - My Books and then Archive.
The "Repair your Kobo Account", removes all purchased books and triggers a download for them. This is probably the most complete sync you can do without losing the sideloaded books. It should fix the problems here. But, I would suggest looking at your library on-line and see what is where. If it isn't syncing, it might be that all the books are in the Archive. If so, you can restore them from there manually, but, I'd be pushing Kobo to fix it.
If this doesn't work, try signing out of the account. You will lose the reading status and annotations for sideloaded books, but, you won't have to sideload them again.
Also, do this on one device. Turn the WiFi on the others until you get one sorted out. Hopefully, the others will sort themselves out when they sync after one is fixed. But, the repair might be needed on them as well.
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