Hey there,
I was asked to add my solution to this awesome thread so here it is.
It's rather simple, check the hip file if you like. Theres a vector "self" (pointing away from the spline itself) added to all points, and a vector "surf" pointing towards points densely scattered on the collision geo but only added to points that got pushed outside of the volume. Finally another vector "straight" is added pointing to the center between the previous and the next point, effectively damping the bending.
Finally I should note that the very last step of the solver is a wrangle that has an animated lerp between the previous' and current frame's shape to safely control the speed of the whole thing in one parameter. Without that it would fill the whole thing in a max of 40 frames and then slow down harshly, but it was too late to tweak the forces and I wanted to render it
Cheers!
BrainGrowth_v001.hipnc