Advice/Help with Support Structure

I've downloaded a model of an ArWing from Models Resource, and spent plenty of hours cleaning it up and making it one solid piece. The problem I'm having is generating/modifying a support structure for it. The first time I tried printing it, using Cura's support structure, I couldn't break the support away without destroying the wings. I've also played around with the support options in MeshMixer and B9C, but the print keeps boogering up lower parts (circled pink in the image). I guess my question has a few parts to it. Should I print the thing standing up or laying flat? Also if anyone has any suggestions for generating a support structure (programs, recommended settings, etc.) I'm all ears.

For some more info... I've had my 3D printer (Printrbot Simple Metal w/heated bed) for about a month now, finally got it dialed in (lots of cubes and abstract shapes later...), and this is BY FAR the most complicated thing I've tried to print. I've also designed and printed a stand for the ArWing if you wanted to know what the hole in the bottom was for.

The ArWing: Attachment 4786
The Stand: Attachment 4787

Have you considered cutting it into multiple pieces and gluing it together afterward?

Those winglets are getting really thin towards the edge, you might have to print the thing out solid to keep from breaking those edges.

I think this is a typical case of models not designed to be printed. The geometry is not complex, you should consider re-designing it from scratch to ensure the proper minimum dimensions for your printer. That way you can choose how and where to cut it to limit supports.