Or paying attention to your NAS on a regular basis. Granted, this is my home network with only like 5 machines connected to it max. (My desktop, my laptop, my NAS, my home-theater PC, and my tablet).

Since the NAS is the center of my important data, I pay attention to it more.

-----------

A business solution would probably need an alarm of some kind, because a busy IT professional isn't going to have the time to baby a machine like I do.

Its just the whole "computers are cattle in professional IT settings" but are "pets for the home user".

Could this kind of attack be thwarted by keeping free disk space to a minimum - such as 15% free space? That way, the attack wouldn't have enough free disk space to happen. This would be difficult in systems with highly-dynamic storage needs, but could be done on application or caching servers.

No.

The attack happens on a file-by-file basis, within the free space that you have allocated on the live filesystem. foo.txt, bar.pdf, and baz.jpg are all encrypted in place, consuming only marginal free space during the operation.

Then, when the incremental backup happens, THAT will notice that ALL the non-OS files have changed and the backup consumption will explode.