I applied the simple practice of sending a follow-up email to leads that didn't confirm in the first 5-10 minutes -- from our email account (gmail), not aweber.
The email mentioned they opted in and requested something, but didn't confirm. I went on to say the reason was likely due to the confirmation message being in the junk box.
So far we've seen a solid 50% recovery rate. We've written a script to automate this using Aweber's PHP API to get the list of unconfirmed subscribers, and we then send the emails from our web server using this list. It appears all of our web server messages arrive in the inbox, like the gmail ones, instead of going to junk like a lot of Aweber's emails.
Very simple and very effective -- it feels like I ran into amazing results by complete accident. I hope someone puts this to use for their lists.
I just got off the phone with AWeber and they said it IS ALLOWED to send a reminder email, as long as it DOESN'T INVOLVE AWEBERS SERVERS, i.e. our own gmail account. They went on to say the information this link only applies to their service/servers.