Any way to make curve-based soft bodies collide?

I’m trying to make an effect like sea anemones swaying in turbulent water.

I started by making a beveled two-point bezier curve into a soft body, and then used that as a hair particle, and then added a turbulence field. The particles move in a way very similar to the effect I’m trying to achieve, but the problem is that, being beveled curves, they intersect.

The collision settings for soft bodies and hair don’t seem to do anything for this scene, presumably they only work with meshes.

I tried converting the curve to a mesh, but then I lose the nice movement effect.

Is there any way I can prevent these beveled curves from intersecting? Or is there some way to create a mesh that moves the same way in a turbulence field?

Here’s an animation showing the curves moving in the turbulence field:

And if YouTube is still misbehaving, the video is also here on Google Drive:
https://drive.google.com/uc?id=1f94TmqVNAzOu_M-JPZzO9x_9z7ZulfIj&export=download

And here’s the .blend file if it helps: 2019-06-04_07-10-11_02.blend (1.7 MB)