Samba domain trust errors on a specific interface

Solution 1:

This may be a highly specific case, and I wish I had a better answer, but I spent a few more hours on this today, and noticed Winbind was turned off. I know winbind was running in the past, as I was getting successful authentications with wbinfo -a. At that time we were still unable to access Samba over private links.

Regardless, after turning Winbind back on, the private links magically started working. Sure enough turning it back off broke them again.

The entire time, though, I was able to access shares over the main LAN connection. I'll still give 50 points to anyone who can explain why that is :D