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Obviously the real email addresses must remain untouched, but I'd like to wipe the slate clean with regards to publicly displayed email addresses.

Can I run a query which will quickly clear this field for all users? Just want to do this as a one-time step, not worried if people fill these in again...
You can use the following query:

UPDATE w3t_Users SET Fakeemail = '';

You must change the w3t_ prefix if you have a different one for your installation.
That would be
Code
UPDATE w3t_Users SET U_Fakeemail = '';  
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