Damian, "new potatoes" won't store until next year, they're too young. You'd be best off eating them before you lose them. Potatoes for storage are best harvested when the plants die down and then either let them cure under ground a few days/a week, or dig them up and let them air-dry for a bit so the skins harden up. And, of course, you'll want to brush them off of any dirt so they are fairly clean before putting them in storage.
Your new potatoes are sprouting because they are too warm and/or not getting proper ventilation. Again, best to eat them and enjoy them while you have 'em.
Patti, the blog you referenced isn't quite up to snuff on some facts. Allowing the spuds to turn green for storage won't put them into dormancy, it'll only cause them to create solanine which is natures way of protecting the potato from insect and fungicide attack. (Ain't Ma Nature smart!? :>) As for dormancy, potatoes naturally go into a dormancy period - under proper conditions - and don't rely on needing the solanine to do so. I think, depending on the variety, dormancy periods are normal for 80-120 days or so.
Damian, if you still have some plants that are producing let them keep on keeping on and harvest the more aged potatoes for your storage and seed stock. Keep them cool (if you can in Florida) around 40ยบ or a tad less, and in the dark with ventilation. I imagine Florida has a fairly high humidity so maybe you can use that to your advantage as well.
Shoe.