Grinding the stump will not cause the roots to move. My bigger concern is that grinding the stump will not kill the tree - you will have suckers showing up wherever roots are within a few inches of the surface.
After you have the tree cut down, poison the stump. Crepe Myrtles don't have bulbs, just the part of the trunk that is underground. In a few years, that part will rot and you can fill the void with garden soil. Or, after you know the tree is dead, grind the stump. Over time, some subsidence could be caused by the decomposition of the roots but this is better than the alternative (trying to dig out all the roots).