Cardboard generally fails in two different ways, crush and burst. Crush is from vertical compression along the tubes, burst is through one face and out the other. A box in a box (even if you Frankenstein panels into the old) is the best solution. Boxes used for heavy use are “double-wall” which just means the wall contains two sets of flutes (the corrugated portion of the box).

Add (or maybe even glue) another cardboard sheet to the inside bottom face? It might help spead the load out a bit.

Not an expert, just thinking it through. Cardboard boxes fall because the load distends the bottom of the box or because the seams fail, in my experience. You can’t just stick one box inside another because they’re the same size, but you could cut one box into sections that are the inner dimensions of the other to make the box thicker and less likely to bend/distend.

You could reinforce the edges and seams with packing tape to give them extra strength.

Probably worth a shot.