Feline,
Not all commands are available as methods, and I would expect the Publish command to be one of them.Some menu items are implemented as separate clients and can only be accessed through CallClient. But they will have to have a client calling mechanism implemented to respond, and you would have to know the syntax. And even then it might not work due to missing or incorrect info (or bugs in the callback mechanism). As an example, I tried to automate the conversion of files to structured FrameMaker and the one command I needed does not repond to the CallClient method (which is even used as the single example for CallClient in the documentation). Frustrating, to say the least.
I am afraid you will not be able to get this working, unless somebody else on this forum knows how to call any arbitrary menu command from ExtendScript.
Sorry if this sabotages your plans
Jang