I do not yet have the process working as I am trying to get a new security certificate from GoDaddy. It took a long time to find an answer but here is what seems to be happening:
The security certificates for changing from Client mode to Admin mode are hard-coded into the AMT firmware and you must use a certificate from one of those providers to make the switch. We have already been using certificates from GoDaddy for other purposes and since that is one of the hard-coded providers I am trying to get a certificate from them. The hold up for me is our own internal bureaucracy. Note that the only reason I found this information at all is because I stumbled across it in the documentation for the Software Development Kit for AMT when I used Google to search for it. The search on the Intel site failed to find anything about this at all.
My understanding is once I have the new certificate installed I will be able to switch modes and then at that point I can start using the internal certificates for all other processes related to AMT. As I said before though my own personal hold-up right now is the internal bureaucracy I have to deal with.