I was wondering something similar, I was trying to find a 3D mandelbrot. Not a mandelbulb, but a 3D equivilant of the mandelbrot set. When searching for it, I came across some 3D 'representations,' but they didn't really appear to be a true 3D mandelbrot set.
Then I accidentally made a 3D mandelbrot, in the program Mandelbulber. I made a hybrid fractal of the mandelbulb, and the 'general mandelbox fold' and came up with this: http://img.photobucket.com/albums/v252/TMTIGD/3Dmandelbrot.jpg
The fun thing about this model is I can enter the X and Y coordinates from the traditional mandelbrot set, and it will zoom in on the same portion of the 3D model. You can even see the dendrites, and self-similar mandelbrots on the dendrites, exactly were they would be in the 2D set.
I'm not completely sure this is what you were looking for, I have been having trouble finding julias sets in the 3D model were I find them in the 2D model, but that could simply be because of the quality settings I'm using. Either way, this is the closest match to a true 3D mandelbrot I've come across. Any others have strange artifacts or artistic fluff that makes me wonder if it's just the 2D set with a lot of pretty effects.
edit:: After playing around more, this 3D mandelbrot is puzzling. With certain settings, I can see the outline of the 2D mandelbrot from a top-down view. If I use too many iterations, the spiraling branches and arms visible in the 2D set disappear and I only see smaller and smaller self-similar mandelbrots. Then if I set certain settings (mainly "DE detection") too too high of a quality on a point were you expect spirals and intricate branches, I am only shown an "oil spill". Then on other combinations of quality settings, I see wispy clouds of semi-transparent smoke over the mandelbrot set itself. (http://img.photobucket.com/albums/v252/TMTIGD/image00384.jpg)
It seems most obvious that with the best of quality, the features from the 2D mandelbrot set are clouded and usually completely hidden when viewing on a microscopic scale.
I would really love to hear more input from someone (especially the question asker). I have a feeling this probably isn't what he was looking for since he appears to be somewhat of an expert in this area, and he hasn't found a 3D mandelbrot-esque figure. I only found this by chance, but it doesn't look like anything he has dismissed yet, so I'd love it my dumb luck happened to find a way to view a 'true' 3D mandelbrot.