That will work, but you're making your life difficult :)
You can add a Service Reference to your project in Visual Studio and call methods in the ASMX service just like you would call methods in a referenced DLL. See this article.
UPDATE:
Yes, your method for calling other services will work, but I would check to see if adding your other services as Service References to your project works first. The service reference feature works with all kinds of protocols (whether built with Microsoft technologies or not).