At first I imagined the question to be how to make a gingerbread dough that would work on a pottery wheel—which is a very interesting thought!
Former pastry chef here, and wanted to say you’re on the right track with your brainstorming! Lots of good advice on here. I know it’s idealistic to use only royal icing (which does indeed dry like cement), but as you even have noticed, it takes a while to dry and there could be some shifting during that time. What the Europeans in this thread are referring to when they suggest “caramel” is just sugar heated until it’s molten and when you use it to stick your gingerbread pieces, it dries incredibly quickly like hard candy. You can always pipe royal icing over it as decoration if you like the aesthetic. But for something structural like this, using royal icing exclusively will just make a complex job harder for you! That’s just my opinion.
As for other pieces, if you wanted a different material, you could always play with modeling chocolate or with pastillage (an edible structural dough made with powdered sugar and gelatin that’s snow white and dries incredibly hard and lasts virtually forever).
You’re doing great!