One trick I've found is to use a bit of cornstarch in the dough—it keeps them soft and chewy. Also, make sure you don't overbake them; they should look slightly underdone when you take them out of the oven.
I feel you! Perhaps, you could mix cornstarch into the dough in lieu of water or reduce cooking time by a minute or two and add cream cheese to the prepared dough. Store them in a plastic container that can be sealed well to keep the chapatis moist and to soften them add a slice of bread. Happy baking!
I think using a combination of brown sugar and granulated sugar in the cookie dough adds moisture and helps create a soft texture! Though, chilling the dough before baking can also prevent spreading and result in softer cookies.