We just picked all of ours. The ones that have seed would be best picked now as you are correct about the mold. Although even if they are dried nicely and then hung back out they can get the mold on them then. My experience is that the birds will eat them no matter what! If you let the unripe ones linger in the garden unpicked you are bound to get a few surprise sunflower plants next year as well as leaving a treat for the birds. I put a couple heads out for the chickens and they were picked clean in no time at all. Fun to watch.