Hi Wimverbe,

I know that others may show you a visual, but try this out:

The problem may be arising from some kind of inaccuracies in the curves. Maybe on a micro-level something isn't lining up.

Take your profile and run the "Rebuild" command (in the text command box at the bottom).

In the dialog, choose the "Refit" option. In this case I told it .001 for the value, but this can be different depending on the scale your model is working at.
Make sure the original object is deleted. It may not be laser-accurate, but it will play nicer with construction methods.

Your profile should now Sweep along your 'L' path. When I tried it, it says it's a "Solid".

You'll still have separate panels because of the right angles, but it should be a manageable solid.