I really had no intentions of posting in this thread (as I usually simply search around the forums remaining introvert), but the last post rendered me highly tempted to reply.
First of all, I truly love the design of the hide, and, as what many others have stated, it renders my tank design quite inadequate. Consequently, I feel a very large temptation to adorn my aquarium with hand-made ornaments, which I will once a sufficient quantity of Java Moss grows.
Now, Snootyfox, although I utilise sand as a substratum, I have an idea that may or may not be sufficient for your issue, and may or may not be feasible. What if you removed all of the sand and replaced it entirely with a carpet of Java Moss? My ideas of ornaments that inspired me from this thread (that involves the Java Moss I have growing in my basement) plus your post gave me that idea. You could purchase some mesh, crop it down to the size of the bottom of your aquarium (or a bit smaller to allow growth), weave fishing line through the mesh with Java Moss inside (you might want to allow the moss to grow beforehand, or simply purchase a large quantity), and use your own imagination to figure out how to stop it from floating at all sides. I have seen fish tanks (no axolotls) with a carpet of Java Moss, though I have not really thought about how it was executed. My idea was just my hypothesis, therefore read other methods if my suggestion intrigues you enough. I have read somewhere that axolotls enjoys laying on Java Moss, though I've haven't personally witnessed this yet (no Java Moss in my axolotl aquarium), and I'm not certain if they would like Java Moss everywhere. Perhaps add a few hard surfaces? These are only suggestions.