All Internet Accounts have disappeared

Hi there,

Yesterday evening I found that all of my accounts in System Preferences > Internet Accounts had disappeared.

These included an iCloud account, 3 x email accounts and a CALDAV account.

The panel now shows as empty...

The 3 email accounts no longer show up in Apple Mail (2 x IMAP Gmail and 1 x POP)

Apple Mail instead now shows the 'Welcome' (Add an account) screen.

However, the ~/Library/Mail folder appears to be intact.

Attempting to re-add accounts into Mail causes Mail to hang on this screen...

My iCloud and CALDAV calendars have also disappeared from Apple Calendar.

The accounts have been the same for at least a year each, and I haven't upgraded macos recently.

I have a Time Machine back-up that's a few weeks old, plus one from today - since the accounts all disappeared.

Apple Support have recommended that I wipe my entire machine, restore the back-up from several weeks ago and then manually restore individual files that have changed in the intervening time from the newer backup.

This seems like a potentially very long process and a heavy handed thing to do.

Can anyone suggest any individual files I could try restoring to fix this before I wipe the whole machine?

Thanks!

Nick

Macbook Pro Retina

Sierra 10.12.5 (16F73)