Thank you David and Chris, I appreciate your replies. Fortunately, I did actually manage to solve this virtual user authentication issue. However, it seems there is still some issue that prevents Thunderbird from being able to download mail from imap.
First the matter of the multiple database authentication issue. My doveconf remains the same as when I last reported it. The major changes were in my postfix login map and my passwd-file for the virtual mailbox. In /etc/postfix/main.cf I have smtpd_sender_login_maps = pcre:/etc/postfix/login_maps.pcre. In that file, I previously only had the first line for my main domain and I had to add a second for the hosted domain:
/^(.*)@example\.com$/ ${1}
/^(.*)@example\.net$/ ${1}@example.net
For some reason this is required to get postfix to recognize that accounts from example.net are valid, or to otherwise be handed off to authentication properly. The other mistake was in my passwd-file at /etc/dovecot/passwd/example.net where I did not properly specify the password format:
user@example.net:{crypt}...long..hash...::/var/postfix/virtual/example.net/user::
With these changes, I am able to login to Thunderbird as user@example.net. I can send mail from user@example.net, and allegedly look at my mailboxes on the server for this user. However, due to some weird quirk I cannot actually collect mail from my inbox on the server.
For user@example.com, who is a linux user with a home directory, this is seemingly no problem and their mailbox is set up according to the configuration:
/home/user/
Mail/
Inbox/
mailboxes/
...indexes and logs...
However our virtual mailbox for user@example.net looks like this:
/var/postfix/virtual/example.net/user/
Mail/
Inbox/
mailboxes/
...indexes and logs...
cur/
mailboxes/
new/
tmp/
subscriptions
...indexes and logs...
Clearly dovecot is trying it's best to make the Mail directory as defined in the conf for the virtual user in their defined home. However, the mail is instead delivered to the new directory which is not configured to be there. This confirms this user is actually recieving all mail sent to it, but because the inbox is not configured correctly (somehow) it is not possible to actually read it in Thunderbird.
From what I've read this pattern (cur, new, and tmp directories) is associated with Maildir, which is confusing because the mail_driver is explicitly set to sdbox. I am not sure how to resolve this, or where exactly the issue is being caused.