In spite of what the Tape and Compass article said about using color, I think it is a fine way to show different levels. I remember seeing Bill Torode's map of Fern Cave, AL, that was drawn using multiple colors . If you know anything about Fern, it has many, many levels, and the multi-color method was probably the best way to distinguish the levels.
Your map is fine, and is certainly not "hideous." However,one thing it does need is a label clearly showing where the entrance is. I am guessing it is where the "0 datum" label is, but for clarity's sake it needs to be marked.
Another possible method to use is an idealized profile view of the entire cave. This can show the various levels of the passages, and is probably easier to do with a cave that is relatively straight, like this one is.
I am curious why you chose to have north inverted. Perhaps other cartographers can weigh in on this, but my practice has always been to have north aligned with the page and pointing up. One map that I am familiar with that has it pointing down is very confusing to use in the cave. Every time I use this particular map, I have to constantly remind myself that it is inverted and should be read upside-down.
Trogman