After some searching I came to the conclusion that the TV needed to have the system firmware reflashed, something that is likely done when Sony services the devices (explaining the lack of documentation for the LED code). Before the board was replaced, the TV was running the latest stock Sony firmware from 9/17/2012, so I downloaded that from this thread here. While I can't say for sure, it would likely be a good idea to reflash whatever firmware you already had on the TV before, especially if you aren't replacing the main processor board. Every Sony OTA update is available in the NSX-40GT1 wiki on this site through a link found under the USB update section.
To do the update, I followed the instructions found here which I have replicated below. The file will need to be renamed according to the particular firmware version that you downloaded. For me that ended up being "package_list_DMA-1_ASURA_2012091701_AAV_ORSC.zip". Asura is the codename for the TV and Eagle for the blu-ray player.
Getting the update started is where things got a little hairy for me. I followed the instructions below to the letter and was expecting the update process to begin and a message to appear on the screen telling me it was doing so. Instead, after powering on the TV I continued to see the two blinking lights on the front of the set. At this point I left it on and turned around to do some more research, only to turn around about 5 minutes later to find the expected "upgrading" message and a status bar indicating the process was nearly complete. The sleep timer LED was still blinking amber, but the power/standby LED was now solid red. At some point the system must have recognized that there was an applicable update stored on the USB drive and begun the update. After the update I was pleasantly surprised to find that this process does not wipe your user data, so no initial setup was needed.
I hope this can save someone else the time and agony I spent!
How to manually update your Sony NSZ-GT1 to Google TV 2.0
- Format a USB thumbdrive as FAT32
- Download the update package Sony Eagle 2011.10.23 from [Google Link] ... V_ORSC.zip
- Rename the downloaded file to package_list_DMA-1_EAGLE_2011102306_WWV_ORSC.zip
- Copy package_list_DMA-1_EAGLE_2011102306_WWV_ORSC.zip to USB drive. !!!Properly eject!!!
- Disconnect power cord from Sony NSZ-GT1
- Plug in the USB thumb drive in the front USB port
- Press the power button, holding it plug in the power cord, and continue holding for 3-5 seconds
- Release and wait. The device will boot, recognize the update, and start the upgrade. Follow onscreen instructions (i.e. do not power down the device while update is in progress..)
@tsella // props to GTVHacker.com wiki and XDA-developers.com for the various pieces requires to put this together