Without knowing further details, it is difficult to pinpoint the cause of the crispiness you have been experiencing, but some of the more common causes include baking at too low a temperature and for too long a time, a lack of sugar in the dough, and little or no oil in the dough. If you aren't using sugar or oil in the dough, you might try increasing the bake temperature and shortening the bake time. If that doesn't reduce the crispiness, then in a future effort you could add some sugar and/or oil to the dough to shorten the bake time and make the crust a bit more tender and less crispy. Even though you are baking on a stone, you could put a pizza screen between the pizza and the stone to keep the pizza off of the stone. This might be done during the last minute of baking so as to reduce the crispiness by just a small amount.
Another thing you might try using you present methods is to put the finished pizza on a flat tray and let it set for a minute or so before cutting. This might drive some of the steam back into the crust and soften it somewhat so that it isn't as crispy.
If you find a solution to your problem, please let us know.