How to get the left hand on the hilt of the sword? (Look video)

My 2c on this is that you already spent way too many hours on it over spanding maybe 1/4 of the time to manaully fix the animation to match the sword.

IK systems are never perfect.

The final hand/bone position is a suggestion not an absoute.

If the rest of the bone chain CAN accomodate the position, then the final result looks OK. If the bone chain hits limits, then the position will be off.

And rotations, like seen on the animation in question with the snapping are especially problematic. Chanches are the rotation itself is causing the snap at least in part.

If you want the hands to always grip the sword your options are to
A) socket both hands and set the bone chanin for the right arm to be physically driven (which may or may not look like trash).
B) manually animate the changes based on the hilt lenght.

Anything else will almost always have points of failiure whenever the bone chain finds a limit…