Danny, that's exactly what I was looking for! I played around with lattices for a couple of hours last night and realised that, to achieve even a mildly interesting result, would require an incredible amount of setting keyframes on lattice points and endless tweaking.

While reading the docs, I discovered the IK Spline Tool and had completed step 1 of your trio. Unfortunately, I was completely stuck on how to grow it... what you propose in steps 2 and 3 is great! I would never have thought of 3.

Many many thanks, I'll be trying that tonight.