Update. An even easier way to stabilize 360 video is now built into SkyBox Studio V2.
See: mettle.com/product/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