Your whoopie sling, at the end closest to the tree, is basically a loop. When you use a MSH you are hanging the loop off the knot. If you don't want to use a MSH/toggle, you could wrap the tree strap around the tree more than once if need be and through the sewn loop on one end, but now you need a way to attach the sewn loop in the other end to the loop formed by the whoopie. I think this is where the soft shackle or biner comes in.... hook the biner to the sewn loop on the tree strap, and hook the loop of the whoopie to the biner?
Seems to me you still have to unhook your tree strap from the whoopie, if only briefly, to get your hammock down. Still you can clip it right back together and put the whole works away in "one piece", or by using a Dutch clip or biner to secure the tree strap to the tree you could even skip that. I've left tree straps behind on the trail so I can see the benefit of this method even tho I like to use the MSH.