Thanks Matt, I'll give that a try. It makes sense, especially if the animation's start and end are a large number of frames either side of the rendered sequence.
As a further note, I tried just one transform node moving the fractal up in the Y, but it looked like the fractal was... moving up through the cloud

So I added a second transform node to move down, offset by a large amount to start with to avoid mirroring, and used the merge shaders node to mix them together (just plugged together without any further options selected). There seems to be a bit of extra softness, but the overall effect is better.