Mark
Firstly, don't disable STP on the access switches. STP is there in case someone create a loop either accidentally or maliciously and you realy should have it running.
Secondly, your etherchannel between the 4506 switches need to be a trunk. If you make it a trunk then gamma will become root for all vlans and delta will see the etherchannel port as the root port for all vlans.
Etherchannel is the technology and port-channel is the logical interface that is created when configuring etherchannel.
Your thinking is correct as far as configuring the etherchannel to be a trunk link ie. add the commands to the port-channel interface and this will take care of the physical interfaces.
One last thing, when you do this there will be a small outage on your network as STP will need to reconverge so best to make the changes out of hours.
Jon