Rabbit **** and vermiculite. I grow some fantastic watermelons and cantelope by cutting plastic 55 gallon barrels in half and then drill drainage/siphon holes in the bottom and add about an inch or two of gravel, add about 2/3 of the remainder with good black dirt/1/3 rabbit **** and about a pound of vermiculite mixed all together and sit it in the spring and it allows for water to sipon up to the roots of the melon plant and run the vine out on dry ground.
Your cardboard idea will work good too, basically doing the same thing as the vermiculite, holding/attracting moisture. I knew a barber who swore by mixing hair into his dirt, he kept all his clippings for fertilizer. I would add some type of manure, whether it be horse, pig, rabbit, or chicken. The tree huggers use composting toliets and use their own composted waste for planting their organic veggies, so you could always dig a hole and fertilize it yourself, a cardboard wouldn't be that bad instead of toliet paper.