Someone (named simply "Don") saw my entry on the origin of the term middleware and was nice enough to email me a reference to an even earlier citation from 1968! The term middleware was used in the famous report of the 1968 NATO Software Engineering Conference:
I'd heard of the famous NATO Software Engineering conf/paper but never seen it. It seems like middleware may be as old as software.
I find it very interesting that in 1968, it was used to refer to software used to adapt generic file system functionality to specific application functionality needs. More generally, I guess you could call middleware "software in the middle of application software and system software."