All suitcases should have two handles -- one on top and another on the side, so you can comfortably grab onto it with both hands. Since they don't, somebody on Quirky made a strap to do just that and it's called Lift.
Billed as a heavy duty t-strap, the contraption runs down both vertically and horizontally down the center of the luggage, secured by plastic fasteners that hold it steadily in place. It's also adjustable, so you can use it with whatever size of box or luggage you're hauling around (not sure if it's long enough for your DJ3K Trunk, but most suitcases should be fair game).
The Lift uses heavy-duty woven nylon straps that measure 1.75 inches wide and 80 inches long in both directions. It comes with four integrated handles that you can move along the length of the straps, so you can have four people carrying a single container if it's a bit on the heavy side. Other features include a seatbelt-style plastic buckle that makes it just as easy to remove as it is to lock on and a luggage tag on the front plate.
Someday, we'll have luggage with quadricopter blades that you can control with a remote so you don't have to carry anything. Until that time, I guess the Lift should do. Since it's a Quirky project, though, they're still waiting to fill up preorders before proceeding to production. You can reserve yourself one for $23.99, with the price going up to $29.99 during actual retail.