Guess there isn't a lot of meaning to holding on to this part of the issue. Here are 2 test meshes courtesy of Greatness7 so the behavior can be compared between vanilla and openmw. I don't know what should be done about lip animation, I would guess morrowind's loudness calculation isn't as clever as openmw's.

interpolation test meshes.zip

Quaternion quadratic interpolation is technically possible and doesn't rely on curve tangents, but my math skills are lacking. It's supposedly not possible to export a mesh that uses quadratic quaternion interpolation using the conventional modelling tools if I remember correctly.

Morrowind does in fact appear to use cubic Hermite spline and NifSkope is correct, although NifSkope's actual rendering does not reflect it. However, Morrowind also doesn't seem to correct morph geometry weight values that don't fit into [0;1] range, which openmw did and which misled me and akortunov when akortunov experimented with cubic Hermite spline (you can see it on the netch mesh).

Here's some info on Hermite splines and also TCB/TBC splines which should be useful for future developments on the issue.