I sometimes have to travel with a box of precious cargo and have learned the hard way via trial and error.
What has worked 95% of the time is taking a thin rope, like a
nylon twine, which you can find almost anywhere, double it up (so now it's two ropes parallel to each other for reinforcement) and just criss-cross the bottom, creating a "+" sign on the top and bottom, like putting a ribbon on a gift. I then create a makeshift "handle" of sorts by either buying handles at Office Max OR reinforcing the part of rope that will be held with tape, the point where the two perpendicular lines meet on the top of the box, so it's easy on everyone's hands.
The easier it is for the baggage handlers to handle (by providing them with some sort of grabbing mechanism) the better condition your box will come out at the end of your journey. I even secure the rope to the box by taping the sides and bottom, forcing the baggage gal/guy to have to grab the makeshift handle.
Without a rope, they will have to grab the box by the edges or the sides, this gives room for it to be tossed, slip from the hands and be dropped and other things (kicked, slid, pushed, thrown). With just a rope, the box can be grabbed from any side. With a rope, sides/bottom taped with a makeshift handle, you have now minimized the odds of the box being handled any other way than the way you want it handled.
Leaving the "hand holes" on the sides open leaves room for the box to rip. Some may try to lift the box with only one hand, which can rip the side of the box open...and I know you don't want that. So, I would close up the holes.
Have a safe move.
NOTE: Write or affix a sticker with your name and info ON the face of each box and have the check-in agent apply the baggage tag to the box itself NEXT to the handle. Do NOT have them put the baggage tag on the rope.