One workspace, two IDEs - Possible? How can I create a workspace &amp; projects so that either the Arduino IDE or the EclipseArduino IDE may be used to develop the project, interchangeably?

I have both IDEs installed and working but in separate workspaces. 

I need:


One workspace that either IDE can understand and work in;
Either to IDE build with the physically same set of library sources;
Whichever IDE I open to see my sources as I last left them, regardless of which IDE I last used.


I want:


The source files to have conventional names - .C or .C++, not .pde or .ino;
Either IDE to build with the physically same set of library object modules;


My use-case is that I work in/with Eclipse, and I teach Arduino skills to people starting out with the Arduino IDE. I'd like to be able to prepare class work at home with Eclipse but open and project it in class with the Arduino IDE. It would be nice if I could demonstrate the two IDEs using the same code. Clearly, I could hack up a demonstration, but I'd rather do it honestly and without sync issues like having to apply twice any changes we made in class.

Update 20 Apr '16:
At @Jantje's suggestion (in the comments below his answer), I created a github issue, "Importing an ArduinoIDE project with the New Sketch Wizard and using same sketch-name, failed." The new sketch would over-write the .ino file with a new, empty sketch.

That issue got fixed in the April 14, 2016 nightly and now works as his answer to this question says it does.
Are you willing / able to work with Xcode? There is a package called embedXcode that enables Arduino development on Macs – I'm just getting up to speed with it, but it does appear to allow you to work either in Xcode or with the Arduino IDE (the .ino file is present and is what you edit in Xcode). In my testing so far it appears that the easiest thing to do is to create a project using Xcode and then you can point the Arduino IDE at the project pretty easily, getting Xcode to pick up a sketch started in the Arduino IDE is currently beyond me.

From the point of view of your students I would think that you'd want to keep the .ino file rather than make them learn about the conventions of C or C++. It would also save you the hassle of somehow managing file names – although you could probably get make to do this for you.

I haven't looked into it at all, but I think you could do something similar with Atom (a quick Google found a blog post called Arduino Development in Atom Editor and an Atom package called nino that is described as a "Toolbelt for Arduino") or Emacs, or for that matter Vim is also like to have some Arduino support.