Problem solved!
It turns out that the lip-sync problem is non-existent when projecting in MIRROR mode. I can only assume that Windows 8.1 doesn't handle Intel WiDi in 1080p for Modern apps for some reason. Perhaps this is related to Windows 8.1 only supporting MIRROR mode in 720p and all other modes in 1080p.
Anyway, all is well and I can live with 720p and no lip-sync issues. 