Do any of current VR headsets do reprojection within headset independently from the game framerate similar to what tilt-5 does? I would expect it to help a lot with minimizing any delays and thus reducing motion sickness. Shouldn't it work even better with VR since most objects are further away from eyes compared to virtual tabletop thus smaller change in shape of them when doing minor head movements?

I can think of two potential problems with VR reprojection that don't affect tilt-5 as much. Virtual tabletop rendered by most tilt-5 applications is closer to being flat surface which can be reprojected perfectly (ignoring pixel density). There is no rendered content to draw on the edges of screen when turning the head left or right, in case of tilt-5 unless your head is very close to the board nothing is rendered on the edges of FOV anyway since the board is in the middle of it. Might not be too much of problem since FOV edges need less details. Simply fading black or generating filler based on edge colors similar to TVs with ambilight might be good enough. There is also an option to render slightly wider FOV to give some buffer area if it means that hitting high framerate isn't as critical.