We are instituting a new policy with custom titles and need to delete/clear all the currently-set ones.
How can this be done easily/quickly?
Depends where this custom titles are stored, if you're talking about the user's custom titles then a query on phpmyadmin or similar will do just fine:
UPDATE `your_BD`.`smf_members` SET `usertitle` = '';
This will reset all usertitle fields, just replace the DB name with your own and if you are suing a custom prefix change the smf_ too.