My best recommendation:
Convince as many authors as possible to crosspost to AO3.
If you can't find them on AO3 (search fanfic titles, in case they use a different username) - send them a PM on FFNet, offering them an invite. Mention the benefits of AO3: better tagging, mostly, but also being able to moderate comments and group fanfics together in series. And that FFnet is kind of falling apart. Also appeal to every author's greatest desire - new readers!
And then offer them an AO3 invite code if they want one. (Of course, this means
you'll also need an account...feel free to bug me for one.)
And absolutely, under no circumstances harrass them about it. If they say no, leave it at that. If they don't respond, don't send them multiple PMs (note that ffnet also broke email notifications of PMs, so it may take a while*). Be nice about it.
* EDIT: PM notifications are working again, it seems.