How to make hair clumps/objects collide with each other

I would like to ask if there is a way of making hair clumps or objects populated with the hair system collide with each other.
I’m trying to create a stylized curly hairstyle but run into the problem of curls clipping into each other after I extrude curves (first pic).
I tried doing it with hair clumps and objects but both clip into each other.
For hair clumps, I tried tweaking Collisions in Hair Dynamics but, judging by the manual, they seem to serve a different purpose
For objects, I created a soft body with enabled self-collision and instanced it using the hair system, but they still clip

Here’s a blend file:
hair.blend (2.1 MB)
Thank you in advance!