Update. An even easier way to stabilize 360 video is now built into SkyBox Studio V2.
Charles Yeager (yeagerfilm.com) explains how to stabilize 360 drone footage in After Effects using SkyBox Studio plugin. He uses the SkyBox Converter module, one of 4 modules for 360/VR production in SkyBox Studio.
This technique is similar to one used by Alex Vasutin (vrvr.pro) vimeo.com/145500598
Download a free demo of SkyBox Studio: mettle.com/free-demo