If I wanted the ports in my port channel to be trunking, do I have to specify "switchport mode trunk" on each port or can I just specify it on the port-channel interface?
On all the interfaces. Different IOS have different behaviour. In older IOS, I used to do it only on the port-channel interfaces. Sometimes you get wiered behaviour if you are coniguring on different switches. As a best practice :
1. Shutdown the interfaces manually.
2. Configure all the ports as trunk ports.
3. Configure the port-channel parameters.
4. Configure interface parameters if required like speed/duplex.
5. no shut the interfaces.
This should work like a champ.