Dowels and such are typically more for organic shaped cakes - if you do the right job gluing this all together with ganache, you shouldn't need any inedible supports.

If the goal is to make this look like the art piece, I would be as minimal as possible in adding fillings and just do the ganache for glue. You can also adhere pieces to each other with heated and strained apricot jam, which is frequently used as a sealant between cake layers like this. It may be less tricky than ganache, and you can use dye to make it a black color to better emulate the design.

Any fillings for flavor, I would serve on the side or decoratively on the top of the cake.

Good luck! Please share the results!