I've done some bed sized quilts (not king-sized though) on my domestic machine. I take an extra step which is a little time consuming but well worth it. After sandwiching and pinning, I BASTE vertically and horizontally. Long stitches that hold the layers together about every 5 inches apart. I start in the middle and work outward (doing one quarter at a time. It helps in holding everything in place and avoids those goofs on the backing. Now all I can do is stitch in the ditch and cross-hatch but it works for me.
As someone else said, roll the side that will be under the harp of the machine and hold it together with the clips then place your machine where the weight of the quilt can be supported all around. I bring my machine to the dining table or set up a station in my sewing room with smaller tables and even stacked storage tubs to the left and behind the machine. I have never stitched around a design in a block; I only follow lines vertically, horizontally, or diabonally across the quilt. For my attic window, I decided to hand stitch because I couldn't figure out a "system." Good luck, you can do it!