This even affects other players and does not reset when leaving the world or disabling model rendering.

Version: 0.6.1.9a, 1.7.10

Please post your minecraft log

fml-client-latest.log

Here's a separate video of it occurring and the corresponding log

Not sure if I am allowed to comment here, but I got somewhat same issue ... and I fixed it.

When I got hit my head position changed backwards, and everytime I got hit, it adds up the distance of my head from my body, but it is fixed by going to: Edit > Tools > Convert Vanilla Parts
(don't forget to restart minecraft before applying this if the model is broken)

The mods I'm using is CustomPlayerModels and SkinPort
(I used SkinPort mod to fix my broken custom skin that I use in this mod, but now it is unnecessary after converting vanilla parts)

I didn't check my logs or your logs, sorry if I was wrong ...

Bit late, but some mods require vanilla parts to work.
However, it might be that the animations are adding up together. I presume that it tries to undo the animation changes when the animation ends, however it fails and only undoes it partially, Resulting in the dislocation. I think a possible solution is to save the original position and orientation of the parts, and whenever the animation is interrupted, we revert to those saved positions.