I've never done this myself, but I've read that for some tricky breaks like cracks in Bakelite, one useful technique is to first glue the pieces together with a cyanoacrylate "super glue". This isn't the permanent fix, but holds it together and set in place while you work on it. Once the super glue sets, working from the backside of the piece, you can then grind a groove into the crack (with a Dremel or similar rotary tool), which is then filled with a slow-set epoxy (such as JB-Weld).
The epoxy is the structural repair, and the roughness and surface area of the groove ensures that the epoxy will have something to bite into. But the face of the part, where appearance matters, will have been untouched by the epoxy, so there is far less clean-up to the part. A hairline crack will remain, but not blobs of epoxy or streaks from attempting to clean off epoxy spillover.