Dear Ann,
Just throw away what seems dead (stalks and old leaves, but go easy on any roots). Wrapping them in newspaper seems fine -- damp won't hurt as long as they don't stay in that long enough to mold. Ours start putting out roots this time of year, and then just sit there through the winter, but you don't have winter, so probably they will start growing and keep growing (I should probably just let someone from Florida answer you that part!) But the bulbs look fine -- they do die down after they bloom in the spring/early summer.
Go with God.
Mother Raphaela