In summary, while most of the auxiliary losses did improve with training suggesting it was learning some structural information, the model's key loss defined on 3D coordinates never seemed to trend downwards (at the time of writing, the model is still training).
Despite failing on that aspect, this project was initially a learning exercise (and one of my first machine learning related projects) and it was a success in that regard. While the outcome is perhaps not as exciting as I had initially hoped, I believe the project code stands on its own so decided to share it here!