I make something very similar, can't remember where I got the recipe, may have been here ages ago, or a link from here maybe...
Anyway, to keep them pliable fresh from the pan, I use a ziploc bag (recycle/washed, I'm cheap like that
), line it with a teatowel then lay each wrap on that and close up the bag while i do the next one. The steam keeps them soft and pliable. To keep the plastic bag off the food I use a small container that I put on top of the wraps, that holds the plastic up a bit. Does that make sense?
And I saw a comment at the end of the blog post about freezing them. I've never tried to freeze them once cooked, but saw an idea to make the dough, divide it into the correct portions for each wrap, then freeze the balls of dough. This may not save all that much time for some people but I like to 'soak' the flour, so I need to make them ahead somewhat and that puts me off making them at the last minute. But I can make up a few batches of dough, let them sit overnight, then freeze.
My family looooove these, they taste so much better than store bought ones!