Chucky, i've used the technique you've described to 'redry' mushrooms with great success. Have the mushrooms simply come into contact with regular (non dehydrated air) or is it possible that the mushrooms have come into contact with the desiccant itself? If they have come into contact with the desiccant it is practically (if not totally) impossible to get them back to cracker powder dry.
Tupperware containers are good, although if you're planning on storing them for a while make sure you check the lid is a good seal (mum's old warped tupperware is not a friend of mushrooms

. I personally like to use glass jars with the rubber seals that are pulled down with a metal lever. You can get these from any $2 type shop or many supermarkets. You then fill the bottom 5cm or so of the jar with desicant, place mushrooms in little mush bags and suspend the mushrooms over the desiccant inside the jar (tieing the bags to the metal lever makes it easy). Place the jar in a dark dry place and there is no way your mushrooms will ever get moist/ rubbery (as this is how to dehydrate mushrooms in the first place).
If you are dealing with larger amounts, food process or coffee grind the mushrooms to a powder. Make sure the machine is cracker dry and easy to clean - read less wasted mushroom powder

. Either cap the powder (best) and throw the caps in a empty vitamin container with several desiccant sachets, or store the powder in double/ tipple zip lock bags with all the air squeezed out and a few desiccant sachets in between each baggie layer. Pedantic mates then store the baggie inside the drying chamber but I think this is going a little overboard. Again store in dry, dark place. Mushroom powder/ shedded mushrooms do tend to reabsorb air moisture very easily, but with the above methods, mates have stored mushrooms for 18+months with no moisture reabsorbtion or loss in potency.
I use Damprid desiccant, you can buy it from all supermarkets and most hardware stores - go for the bulk pack that looks like a big milk carton, its cheaper and you don't need the stupid bucket that most smaller packs are sold with.