IPad displays incorrect amount of free storage space

The amount of space the OS needs is neither fixed nor predictable. It depends on a huge number of factors: what programs you run, what you do in them, what background activity they trigger, what background activity happens for other reasons, etc. Hard drive space is used for overflow from RAM, logs, temporary files, etc. If the system reserved a fixed amount of space for this, it would wind up being bigger than it needs to be a lot of the time (and hence waste space), and too small some of the time (which would be very bad).

Ok, so after posting this question I had some major breakthroughs, most of which are posted in the update to my question. By then remembering that du still reports in units of 1024 whilst OS X now uses 1000, the final 7 GB was accounted for (well, there's still a potential 500 MB missing judging by Disk Utility, but that's probably just an artefact of du counting in blocks). Now the only question left is why System Information is reporting a substantially lower value for Backups than it should be, and whether or not it will remember to eventually clean up the other 18 GB of local snapshots.