Joshua, there must be something going on to make so many normally non-bulbil producing lilies produce bulbils. Though I try to shy away from those that are bulbil priducing, most of the ones that I do have don't start producing the bulbils until just blooming or after. Usually, I just remove and discard them, since I don't what them spreading all over the place. But, If I want to replant bulbils, I wait until they are ready to pop off by themselves, since that will be when they are the largest. This is always well before the stem starts to dry.