I found a way to gain remote access: My image included a script that automatically joins the computer to our domain. The script ran and the machine rebooted.
I then pushed out a quick n' dirty GPO-and-dirty GPO to that computer which ran the following as a startup script:
reg add "HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\Terminal Server" /v fDenyTSConnections /t REG_DWORD /d 0 /f
That turns on RDPRDP, and I was able to log in as administrator and install the appropriate drivers.