From someone that routinely works from my Jeep.... I'll say a HARD no to the Jammock. I have two, one for the front, one for the rear(I don't have the soundbar. It can be fun to sit up there for a quick lunch, but laying like that model.... it will hurt your neck and legs, even with the pads.
I ended up purchasing the JKloud and LOVE it. You can use it as a sunshade over the rollbars or use it *inside* the Jeep as a hammock. I push both seats forward all the way and I can comfortably hang in the rear. I'm a few inches shorter at 5'10", but I have more than enough room and can't imagine you would be too tall. If it doesn't work, you end up with a high quality sunshade.