The solution that works best for me is the following:
Open the groom asset, go to the LOD tab and set the Binding Type to rigid.
That way, you do not have to go back to hair cards or anything.
The only thing that will not work is the hair moving when the skin moves, e.g. when you do some expressions that involve the forehead that would influence the hair a bit.
Other than that, is looks like the best solution for now.