The actual slicing took about 5 minutes, and the it took 6 1/2 minutes to write the gcode file, because the resulting gcode is over 220MB.
Prior to slicing, I rotated the model 90° on the "X" axis, this way it actually has 3 points it "sits" on, so I added a bit of a raft, and a brim to give it something to stick to. This should be printable without any kind of support.
However, there are quite a few flaws in the resulting slice. There are some missing parts at certain intersections. This is NOT because the object isn't manifold, because it is, it's because there are hundreds of holes occurring at just about every tube intersection. So I imported it into NetFabb and closed all the holes, only this introduced some 1380 non-manifold vertices which I fixed using MeshLab.
Anyway, the new model slices beautifully, and it looks like it's quite printable, except it looks like it would take 28 hours to print it, and it would use 70 meters of filament. The resulting Gcode file is 241MB.
