Conventional storytelling in visual media is all about directing the viewer's attention to where you want it.
Back in the 1990s I did some work with VRML and found that with the user interfaces of the time the user would usually turn his back to what he was supposed to see and then not be able to find it.
If you wanted to break the "looking ahead" pattern you'd want to design the scene so that important events happen in different places; one thing you will need is good audio cueing, and "stereoscopic" sound in headphones rendered by HRTF won't be good enough -- you probably want 22.4 sound, but a properly mixed 5.1 track and an optimal speaker system might be enough.
Also I have no idea how you light a 360 degree scene, both in the sense of "everything looks good" and "you don't see the lights".
Even in outdoor scenes, Hollywood-quality work requires the use of lights, reflectors and other tricks -- if you use real actors and don't light them well they'll go to the union and complain.
There is a large precedent in video game storytelling but even there, critical moments in the story are usually in cut scenes or rendered using "Visual Novel" conventions.