you don't have to do starting and stopping to make it look like that... you mark a few crosshatch lines and then you quilt UP TO the applique, quilt along the outline of the applique till you get to the next crosshatch line, now go back along that line... they will appear to be continuous when you get all done, but will not be. Now the good news.... even the old fashioned crosshatched quilts were not continuous... the lines are predominantly place on the bias... you CANNOT put long, uninterrupted lines of quilting on the bias because the fabric will stretch, the thread will not and you have a problem. So most older quilters (I'm 66 and my grandmother said 3 feet) quilted in predetermined lengths and knotted and began a new pc pretty often... the crosshatch line, outline to the next crosshatch line and back along it, will work well.... BUT
consider the angle.... I have had the most luck with crosshatching when i looked at my appliques and used a line that seemed to have some relationship to the angle on the applique. Are there leaves or baskets or paisley or bears???? If so, there will be a predominant line here and there and if you use that line and a corresponding one in the opposite direction, it will be enormously more complimentary to the actual applique... appearing to have been designed precisely for your quilt.... which it will have been...
one more thing? buy a yard and a half of clear plastic from the fabric dept at WalMart.... buy dry erase pens.... lay it flat, draw several sets of grids.... or any other quilting stitches and then lay on top of quilt.... do one last area with the 'custom slanted crosshatch'.... it really helps you visualize what the quilting will do for the quilt... i do this on almost every one i make.... i bought a yard and a half because it is 54" wide so you have a large square to work with, big enough to put several designs on and you can slide it around to see different effects.... put colored tape on the edge of ONE side... this keeps you from accidently touching your quilt with the dry erase side...