Just to update this thread for the record.
In the end I used Loctite 480. Given that oxidized surfaces don't suit 480 well, I abraded the crack edges gently with a sheet of #10000 grit micro, and painted the 480 on from the inside. As with the account above, I relied on capillary action for the bond to fill the crack. I then squeezed it together for 2 minutes.
The Loctite pack says the initial bond should be secure within two minutes, and then it would take a day to set properly. I timed the squeeze for two minutes, but, as soon as I released the two sides, the crack sprang open again. I wiped it off the best I could, and reapplied. The second time I used a clamp, but I was dubious about the chance of success from the start. The clamp is cheap and badly aligned, and easily exerted too much pressure on the cap. Erring to the side of caution I probably set it too loose, and the result was similar to the first try.
On the third attempt, I tried doing it by hand again, failing again. There was slight deformation of the cap where I squeezed it in. It immediately regained its shape when I released it again. The final and successful time, I used the toothpick and elastic band combination you can see in the picture. I bound it quite tight, by slowly adding to the number of toothpicks inserted into the band. This evenly and roundly distributes the pressure around the cap lip.
I left the cap for twenty four hours, and then cleaned off the residual bond (not that there was much) with the #10000 again. The cap now seems firm and very well shaped. Note I did not have to deal with the barrel/cap threads, as they are set well back on the 12. In the two weeks of daily use since the repair, I have noticed no irregularities and it seems fine.
You can still see the crack with the naked eye, but it doesn't stand out.
The successful part of the process took about half an hour.