I had a quick look at the code (when I first replied), and the documentation (today) for asternet, and, as it is is inadequately documented in the wiki, the code for action_command() in main/manager.c. Although I haven’t worked all through this, as I don’t really want to learn asternet, it looks to me as though you need to use this variation on SendAction:
with the second parameter suitably configured. I imagine you can get ManagerResponse object out of the process, although probably not trivially (I don’t have the time or inclination to work through the whole process).
It looks like ManagerResponse doesn’t have any specific knowledge of the Output: headers from the AMI command action, but does have a general GetAttribute method for reading back arbitrary headers. I couldn’t find the implementation, today, so I don’t know how it handles the multiple headers that I believe you will get, based on reading the AMI code.
As I think I already said, this isn’t really the place to ask about how to use asternet. People here may know the PHP class libraries, but the chances of finding a .Net library expert are slim.