Ann, I totally agree with drying seeds in paper until they are really, really dry. Then the plastic Ziplocs are OK.
I usually store my Ziplocs full of seed inside plastic tubs, and keep some silica gel desiccant in the tub. That way, the very gradual diffusion of humidity through the Ziploc continues to pull humidity out of the seed, and they get down to 20-30% relative humisity instead of staying around 50% RH.
