At least 5 years ago, I designed during a week-end project a coral-like structure.
You can find it on shapeways :
It doesn't take the same approach as you. But it still posed as an optimization search. But as you have noticed, doing the full optimization yields some regular structures, which are not as interesting. So the trick is to stop it before convergence to get a richer structure with some regularities.
In my case I constrained the various nodes and branch nodes on spheres, made the tips spread out over the sphere, while preserving the tree structure, but trying to shorten the branches. The resulting optimization problem gives the upper entangled mesh which progressively gets untangled.
Fun little anecdote : when it was designed Shapeways pricing policy was cost proportional to the volume of material used. My object being of wiry structure, its manufacturing cost went at least x5 when they decided to count the volume of the enclosing box.
Given the way they're generated, is it possible to take several specimens and 'grow them together' so that they're shaped by mutual interactions? The way you've modeled it makes it look like this might be an option.
Talk about self similarity!