Update:
I worked with Avaya, and, I was finally able to upgrade these three phones.
I uploaded a new file to the CLAN TFTP (via the Avaya TFTP server). Several times I plugged the phone in, and, it went immediately into a download, and, then failed. Display TFTP-Server showed that the file was no longer on the board.
I uploaded the file back up to the CLAN, busied the board, and, did a reset on the board. The phone was plugged in, and, just as I was going to release the CLAN back into service, I glanced at the phone and it was seriously into the upload. I did nothing while I watched the phone finish it's upload and come up as a V5.0 phone. I plugged in a second phone, and, it, too immediately went into upload (without the need of the feature access code). It, too, appeared to be taking a good upload. Just for grins, I released the CLAN board, and, the upload stopped. I busied the CLAN again, did a reset, and, the phone started to upload. I now have three good phones.
Please note that this is not the way this has worked for us numerous times before. Tier III said that perhaps the developer tossed an "auto upload" feature into the phone to address customer complaints of having trouble with installations with larger numbers of phones. He is going to escalate and try and get us an answer as to why it is working that way, and, he is also going to talk with the developer.