How to shrink-warp particle system hairs above an emitter?

Hello, I created a haircut using Blender’s particle system, but a part of it is clipping through scalp:


Is it possible to somehow shrink-warp all hairs that clip inside an emitter above, without destroying the particle system / converting hairs to strands?
Grooming hair strands higher above doesn’t help much because each strand interpolation takes a wide area and hairs with steep angle close to scalp slip anyway.

I usually create a Scalp by copying the areas of the Head Object where I want hair to be. Apply the particle system to that and then shrink-wrap the New Scalp to the head…

The Hair should sit right on the Mesh Faces when Particles Hair is created. The combing is probably the cause of the clipping…it is far better to re-comb the hair to get it Back out side… Use hair dynamics > Collision, to get them back outside?

Make sure to check your Normals …

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I just found a video on the Geometry Nodes Hair …that has this covered…
So just in case you want to go that direction take a look at this…