It depends on what and how much you are going to put on them. A thicker hardwood will hold a a ton. Melamine will sag. And probably not an issue, but if the melamine or plywood get wet that can cause other issues.

I would use 5/4 Poplar. Any decent lumber supplier can make the shelves in the size you need. The cost would should be comparable to high quality ply. And less labor. Google "hardwood supplier" to find one near you.

No worries about finishing the edges, plus Poplar takes paint great.

Your looking at the solution, do the same as how the handle was fixed to the shaft. Drill a hole in each end of the coupling nut and shaft, while in place on the shaft, and stick a roll pin through it. It's reversible and cheap and easy.

Any of the other suggestions (except for welding) will loosen up at some point.