Hi JEAE21,
The locking plastic things are called 'cable ties', 'wire ties' or even 'zip ties', they're good for holding shapes made from 'eggcrate' together. [careful though, some of the better quality ones have a metal locking clip, and I'm not sure if they are stainless, so possible rust.]
Eggcrate is quite cheap and available at most home depot type stores, or lighting stores. It is mainly used as a light diffuser in 2'x4' fluorescent light fixtures. In aquarium DIY it is used for 1.74563 gazillian other things. It is very light, and quite durable for its weight. You can cut it with a small hand-saw, side-cutting pliers, or even a good set of kitchen scissors. Rough edges can be cleaned up with a small file, or some sandpaper [or even one of those pumice stones women use to file down their bunions...]
On the bottom of your tank, eggcrate will serve to protect the glass from heavy falling objects, but in the case of your fake rock, I don't think you have to worry. The 'holes' in the eggcrate are about 1/2" x 1/2" [or 10cm x 10 cm] so if your turtle is small, his little feet might get stuck, if he's big no problem...
You could use the eggcrate to make a box type structure to place the rock on, that would be similar to the collapsible storage box you posted, and use the cable-ties to hold it together. Be sure to not leave any sharp edges when cutting the zip-ties, they are famous for that, but your pumice stone can make quick work of them.
If aesthetics is not a huge issue, why not get a big tupperware and turn it upside down and put the rock on that? Things that are food-safe are usually safe to put in any tank. Can't say the same for stuff designed for other purposes [eg. your collapsible box...]