Is there a pattern posted somewhere for making a synthetic quilt with a differential cut ?
Not that I’m aware of.
Also, how often should the various Climashield insulations be stabilized ? Is hooking the insulation to the shell and liner with yarn loops the best way ?
People use various stabilization patterns ranging from none (ie: only attached at edges) to overkill. The norm is 12 to 18” with climashield. “Best” is a loaded word, but yarn loops are quick, easy, effective, and recommended. Because yarn loops fit snugly and do not compress the insulation they do not appreciably contribute to heat loss.
Finally, will running a Climashield quilt through a front-loading washing machine cause the insulation to soften up and drape better ? Will washing the quilt also reduce the loft of the insulation a noticeable amount ?
Wash your quilt in a front-loader without worrying about a loss of loft. This is speculation on my part, but I suspect that success in ‘softening’ up XP would entail damage to the polyester fiber and a change in insulating properties.