I have no concrete ideas at the moment, wish I had
Thinking out loud :
It depends on the loads you want to bear. A structural element of a construction is different from a facade in this regard...
Unlike plants (trees) and corals, where the adaptation of their shape to the environment/medium is pronounced (growing in order to sustain themselves and promote chances for reproduction), the adaptation of the shape is a lot less pronounced for fungi. What is the most determining factor for the shape of fungi : the substrate it grows on?
It seems to me that you would want to control the SHAPE of substrate it grows ON and the "shape" of the medium it grows IN (air, water...). How do you combine them?
How do you conceptualize fungi in order to think about them growing? Making analogies... Is the mycelium like the roots of a plant? Is what we call "the mushroom" in day to day life like the fruit of a tree and the spores like the seeds? Or is "the mushroom" like the tree?
Thinking of controlled randomness and also because I like art, I keep thinking about action painting and the "bird nest" olympic stadium by architects Herzog & de Meuron:
Growing multiple similar rigid layers on the same 3D surface, one at a time, and binding them together afterwards?
Specifically for your research : are you in contact with the MeMC department of the VUB and with a mycologist?