I figured out the problem. 🙂
Both machines are VMs, so I was using a folder on the host machine that was shared to each VM so that I wouldn't have to have both VMs up at the same time. I can't remember which one, but AdminStudio or InstallShield failed when trying to install to that location, so I just made a copy of the Repackager folder in that location and redirected the AdminStudio Shared folder there as well. I ended up creating a new virtual hard disk and made it available to both machines, then pointed the Admin Studio installer to that second disk.
I think the problem may have been because the host machine is not running Windows, so the shared location from the host was not a native Windows file system type.