Yes, you can flip the singer over and use it that way. It makes absolutely no difference to the hitch how it is positioned. A 4 inch drop stinger is also a 4 inch rise stinger. That is how I use mine all the time.
Keep in mind, you want the trailer as level as possible. Using the jacks to level the trailer is not the thing to do. That could possibly overload your front axle and affect the way the truck handles. If your stinger in the rise position makes your trailer tongue high then I would use it in the down position.
One other comment, The Hensley probably is not much lower than the lowest point of most other WD hitches. It just looks that way. Have you actually measured the differences? I have never had a problem with mine hitting the ground or speed bumps.
Barney