After spending a bunch of time I don't have on troubleshooting this issue, I finally got it to go by manually mounting the ISO.
A. Follow pre-upgrade procedures as normal (Shut down, disks-->Dependent, snapshot, restart, etc.)
1. Attach the upgrade ISO to the appliance
2. SSH into the appliance and su to root
3. On my appliance, the vCDROM is /dev/sr0. Yours may be different
4. As root, type mount /dev/sr0 /mnt/auto/cdrom
5. Wait a few minutes. Now, when you do a df -h, you should see the ISO mounted.
6. Wait a few more minutes, then go into VDP configure and perform the upgrade as usual