I may have found a solution (which is weird because I thought I tried this earlier). Setting up the nHair automatically connects the follicleShape and the outputStartCloth mesh, even if the outputCloth is selected.

So, I just rewired the connections (.outMesh > .inMesh and .worldMatrix[0] > .inputWorldMatrix) and the follicle now follows. I though it might screw up the simulation, but it seems to behave the same as before... for now at least.

The below image has the outputStartCloth mesh at the top (the input mesh) and the outputCloth at the bottom, with follicle AND hair attached.