I was actually thinking about how this might be done. It's definitely not a missile that flies backwards but what if it was the function of the pylon? This pylon holds the missile in place by 2 points: one near the fore and one near the aft. When a launch at a rear-target is ordered, the pylon may have a spring mechanism that ejects the head of the missile more forcefully than the rear by a calculated amount that results in the missile's head swinging down and to the rear nearly 180 degrees instantly after the missile leaves the bay. The missile can then activate and launch normally facing the rear.
I'm not saying this is any existing technology but it is a design that I imagined for a rear-firing missile.
Well the high off bore-sight missile might do the trick?? I have rather grave doubts?? but it will shoot an aircraft well off the centerline.
on the other hand, I'm afraid your missile would likely break up, and if it didn't, might not be able to start its engines,,, maybe someone can help you sketch your dream on paper and post it??
to fire a high off bore sight missile and hope to hit anything, its much, much better to have an HMS, but unless you're flying the F-35, there's no guarantee that you would see him directly behind you???