He helps those who help themselves...
I used Ethereal to sniff the packets going between Axon and the GXP2000. No matter what the setting was that got entered into the local SIP port for the GXP200, it would send its SIP packets to port 5060. Axon had been configured to listen on 5062 and hence no registration was being made. As soon as I changed Axon back to port 5060 the GXP200 registered immediately.
I note that in the advanced settings page of the GXP2000's web interface there is a field to specify the RTP port. The SIP port is specified on each of the four separate account pages, and these are logged in Axon as entered. Apparently, these Grandstream phones only send to SIP port 5060.