Twine in and of itself is fine/safe to use, as long as it doesn't have a harmful dye (although I believe most clothing dyes are safe). If you go this route I suggest considering fishing line. It's very strong, very thin and clear.
Swede, I don't understand your suggestion... silicone "seals" as well as "glues" our tanks together...
It's very true that silicone does not adhere to all surfaces, but it will adhere to both wood and rock just fine. I have several rock structures that are glued together with silicone and have been holding up for years.
Gorilla Glue is also safe, I'm not familiar with Sumo Glue. I'm suing Gorilla Glue on a project now Gluing Styrofoam pieces together to form a background/structure which will later be covered in concrete. Gorilla Glue is working very well for me in this application, but it's not meant to be applied in thick layers so I wouldn't see it being a good product to use to glue an irregular shaped piece of wood to an irregular (or flat) shaped piece of rock...