What is eating my HDD space?

[birdman]

which is invisible to 'ls-a', but is reclaimed by fsck or a restart.

If it's reclaimed by a restart then something has a (large) file open that has been deleted. The space won't be freed until the file is closed, which will happen on a restart (and in the meantime the process that has it open can still write to it and use more filespace).

You can find open-but-deleted files by running a find command on the box (which I'll work out if you're interested in running it).