I've never tackled such a repair, but have found quit a bit about it from sources pertaining to old radios, cameras, and even vintage cars.
Here's an excerpt from a British site:
"Advanced bakelite repairs It is possible to repair broken bakelite in a way that is very hard to detect. The first thing is to make solid joints and if you are lucky, you can piece the bits together and glue them in place with superglue (cyanoacrylate). Doing this slowly and carefully is the main secret; it may take quite a bit of 'dry runs' to get the three-dimensional jig-saw to go together properly. Plasticine will help keep the pieces together while the glue cures. For pieces under mechanical stress, superglue will probably not work; in this case you will need to use a modeller's drill to make holes for inserting short pieces of wire to pin the joint in several places. A traditional slow-setting epoxy glue such as Araldite is used to make the joints and this can be built up behind the joint out of sight to give added strength. When nearly set, surplus Araldite can be trimmed away with a sharp blade. An alternative method which also has a lot to commend it is the use of glass-fibre cloth and resin (bonding paste), as used for patching car bodies. The materials are used on the inside of the case to be mended and the trick is to use a file or grinding tool to thoroughly roughen the surface. Using a putty knife or wooden spatula, the roughened area is then covered with a thin layer of resin (about 1/16th inch thick). A piece of glass-fibre cloth is then pressed on, smoothed out and left to cure. Once fully set another thin layer of the bonding paste is spread over the cloth for extra strength. This can be sanded for a smoother finish if desired when cured. Yet another possibility is Loktite BlackMAX adhesive, which is a cyanoacrylate that has rubber dust loaded into it. This helps the impact resistance and also gives a black colour. Some hairline cracks will remain and these can be filled with the self-curing black resin body-filler paste available at auto accessory shops. Once cured you can use very fine wet-and-dry paper (as used for car body work) to smooth the joints until they can no longer be seen or felt. Finally polish with Paste Polishing No. 5 (Baykobrite). For brown bakelite you could mix artist's powder paint with clear epoxy glue but be sure to mix in the powder extremely thoroughly."
Whew! Here's the link to the whole thing: http://www.thg.org.uk/info/plastics.htm
This came from a vintage camera forum:
"Bakelite is basically one huge molecule. You can not dissolve that! If you want to glue bakelite, sand the area to make it rough and use slow epoxy. If you want to achieve a good bond, do small holes with a dremmel around the crack and "sew" the crack with copper wire before applying the epoxy."
From an Australian radio site:
"Iíve normally used 5-minute Araldite but with the rubber strap employed, the longer setting version could be used. If you have any doubts about the freshness of your Araldite, open a new batch."
A British radio site:
"Repairing Bakelite cracks is one of the most difficult tasks in radio restoration. Anyone can glue a crack together using 'Devcon' plastic weld. But to repair a crack so that no marks are left behind is another matter. A Dremel tool is used to make such a repair. First you would cut a grove along the crack and save the dust. Also grind some more plastic dust from somewhere inside the cabinet. Mix with clear epoxy cement and fill the groove over the crack. Grind or sand the cement down. Then polish with rouge to get an even polished surface. It takes a lot of practice to get the expertise needed to make such repairs a success."
Regarding bakelite distributor cap repair, this was posted in a vintage car forum:
"If you grind out the crack with a V using a Dremel tool and fill it with 2 pack epoxy it should work OK. Use a product called Araldite or a similar product, but make sure it's the 24 hour stuff not the 5 minute. We used to do repair jobs all the time in my early years as an electrician using this method. A problem you will have is that the glue will tend to run out before it sets. Use a heat gun ( or hair drier ) sparingly to heat up the mixed glue before you add it to the joint. And maybe work it a little as it sets over a period of a few hours to keep it in the crack. Once it goes off leave it alone until set completely, usually give it 48 hours to be sure."
A vintage radio site:
"Clean cracks and breaks can be successfully repaired with a little superglue. Do not apply the glue directly from the bottle, as you will get far too much. Place a few drops on a piece of scrap card, and use a pin or piece of wire to apply it to the crack or break. In the case of a crack, apply the glue to the inside of the cabinet and let it work its way into the crack by capillary action. Once the glue is thoroughly dry (allow several hours), any excess can be gently removed with a razor blade or modeling knife."http://www.vintage-radio.com/repair-restore-information/general_restore-cabinet.html
Found this from a site that kept crashing my computer...they don't get a link.
"Superglue is only suitable for repairing clean breaks, and is unable to fill even small gaps. If the broken parts do not fit cleanly together, you will need to use an adhesive that fills the void. An epoxy resin such as Araldite (the standard type, not the fast drying) is suitable. Any excess can be removed with a modeling knife once the glue has dried completely (at least 24 hours)."
Many references to "Araldite," a substance I'm not familiar with. Usually mentioned on British or Australian sites, it could be a trade name not used in the U.S. (or I could just be out of touch!) For whatever reason, the Brits seem to address bakelite issues more often than Americans, so many of the products referenced are unknown here. Most of this is in regards to more complex repairs than you're faced with, but I thought that determining the appropriate type of glue/epoxy to use with bakelite would be a key to success. Applying to the back also seems wise from an appearance standpoint. Of course, one could always take the coward's way out and replace the cap! Nah.
Although he specializes in 500s, Dennis knows his stuff, and might chime in with some good ideas.