I've worked some construction jobs, here are some things that popped into my head - I would fill it with something that will resist the copper from denting, so expanding foam is out. They sell a product made to rubber-coat your hand tools (like the handles of pliers) its gone off in the bottle on me before so that might work. You could fill it with fiberglass (chopped fibre glass) and resin.
Why not sand anyway? I think clean sand would be the least messy, as it would blow away, could be brushed or hosed off anything were it to escape.
Commercial kitchens are now often coated about half inch think with a pour/spray on compound, its like a urethane. Very durable.
I know there are stores that sell nothing but stuff related to coatings, resins, paints plastics so you could go from there.
I would put something like a filler (like airsoft pellets) then go with a flexible, liquid binder like a gel or resin, assuming you can fill the whole rack from a single point when its tilted.