Great article, Margaret. I had not remembered it being complicated to get Am's to re-bloom. Here in FL - and in much of the Southeast - they act just like spring bulbs up north. Go dormant in our cool, dry winters and jump up to bloom in March or April and yes, they multiply and make nice clumps eventually.
One thing I have noticed, though is that the foliage sometimes stays green on the plant all the way through the winter. So it's not necessary to withhold so much water that all the leaves die off. As long as it's cool enough, (but not freezing) the plants are dormant even if green leaves are hanging on.
We had a very long, warm fall, and now a cold, wet January so mine were late to go dormant, and are now being lazy about waking up. I have only one putting up a flower stem so far but am not worried, just have to be patient.