You can use drywall "snail" screws instead of duct tape to pack cardboard boxes. It's as simple as that.

Step 1: Poke Dat Hole

Just poke some strategically positioned holes with a screwdriver, making sure you're going through all bits you need...

Step 2: Screw Dat Thing

and screw those snails in. They will hold really well.

Step 3: The Origin

Initially I wanted to use these things. Those are little plastic corkscrews that went with the bottles of wine. You don't need a s screwdriver if using them, but a problem is that I haven't seen those things for, maybe, 15 years, so, I don't believe anybody would be able to possess such devices... unless they have a 3D printer...

Step 4: Constructive Afterthoughts

So I was keeping thinking of those corkscrews after posting the instructable, and here something I came up with in case somebody will actually decide to 3D print them as cardboad box screws.

A flat bar on the top would be more than enough to screw the whole thing down (comparing to those protruding "ears:). It lays flat on the surface of the cardboard, so you can stack boxes ontop of one another, but it yet has enough of thicknes to grab it fith the tip of your finger or a nail.

Also I had this idea of having holes on the ends of that bar so you can put two or more screws on opposite flaps of the box (or other spots if needed) and than lace tham together with a string. The ends of a bar are elevated (bent upwards) to make it easyer to thread the string through the holes.

Also I would make (this is something I wasn't able to replicate on my mockup) that circle shape under the bar of a bit bigger diametre, and make it the one piece with that bar, while also adding a little bump on the top to make the centre part the same height as bent ends of a bar... Just ask me in the comments if you're interested and I'll make a sketchup model to make it clear.