The first model had all normals flipped and several errors.
By reversing all normals, at least it looks ok in meshlab, and meshmedic (shapeways upload fix thingy) is then apparently able to fix it.
I used meshlab 1.2.3b,l loaded the file, and then : menu filters -> normals,curvature.... -> Invert faces orientation, I think I used the original STL.
(guidline in meshlab : the real dark faces are usually inside out, the whiter ones are ok.)
The last wrl file is partly dark partly white, indicating mixed normals.
There is plenty other options, also a re-orient all faces coherently.
But I'm not sure how you got the model partly inside out like the last example ?
As Artur suggest, better contact support, because don't know why the 3d-view still refuses.