Why you have no other option than the Management portal is really beyond me. It seems very awkward for a C#/.NET developer to go back to Notepad style programming with console.log() debugging.
What I would love to see is some Node.js entry points that you could connect to a regular C# assembly which could fulfill the request (as in ASP.NET MVC or Web API) having the full .NET Framework at your disposal.
What I could see as a possible architecture is to have:
ASP.NET MVC hosted on Azure --- writes processed data with logic to ---> Azure SQL DB <--- reads from --- Azure Mobile Services ---- bridge to ---> Mobile devices
Or
Cloud Worker Role on Azure ---- crunching/processing ----> Azure SQL DB <---- reading/writing raw data ---- Azure Mobile Services ---- bridge to ---> Mobile devices
You can use the Mobile Services facility for mobile devices facilities, scheduling and push notifications with limited code and do most of the coding in a managed .NET environment.