How about titles are enabled, but only mods/admins can edit them? Set up one thread somewhere in the Support forum for people to post their requests, and have a mod/admin configure the titles at their leisure. This way, people can have their titles (within reason, obviously, as each one is manually approved this way), and people can expect to have their title adjusted in 24-48 hours or so (though I doubt it would take that long for a team of staff to go through a simple list and edit people's titles). This way, whoever is available and has time to set a few titles can do so, and the workload is spread out.
Also, I really doubt there'd be a huge amount of people jumping on it all at once. Nothing that wouldn't be controllable.
Just my two cents.