Coincidentally, I'm also using a new HDMI/4k LG TV with Free Sync but again NOT experiencing this issue, setup is about 8 months old at this point.
I'll double check my graphical settings for you when I get home though. If I remember right I'm set up for 1080p for the higher FPS but didn't turn off the headlook/hands stuff.
In the mean time clear your cache and keep your Xbox totally powered down for 2-5min at least. Make sure all your updates are applied so your Xbox isn't trying to do anything more than play the game.
Lastly, I keep my xbox up on these little rubber feet which help with cooling and prevent static electricity issues in my play space. I don't think everyone HAS to do this but I for me it's helped.
https://www.amazon.com/dp/B075F1HW3S/ref=cm_sw_em_r_mt_dp_U_cmeqDbP5SCWT5