Main result unpublished at the end of the PhD
You should publish it, independent of your future carreer plans. But of course, journal papers help for postdoc positions!

I would recomment to write a first draft and send it to your supervisor. If you feel about it, ask him, if you should contact the big boss of theory B as potential co-author to strengthen the paper. If he agrees, you could at least get one feedback. 

Usually supervisors are becoming more active if their name is on a paper - they don't want it to be low quality. But maybe this is the problem of your supervisor: Since he is not into the topic, he might not be able to judge whether the paper is good or not. Therefore you could offer to publish the paper as single author and just mention your discussions in the acknowledgements if he prefers this. But I would leave this open as a last ressort.