What makes you think it's a tweeter for audio applications?
I'm pretty sure, and will wager my stake that it's a transducer for some kind of sonar or some other industrial ultrasonic application.
Mr Ling liked GSA contract cash, and i'm sure while under his command they attempted many impossible things for the DOD.
The only other thing i can imagine given the high stability mounting is it had something to do with a delay tube. But, AFAIK the delay tubes were built using off the shelf Altec compression drivers and microphone elements, and were likely obsolete by the time that LTV piece was made.
I have seen much larger, similar curiosities from the same green hammertone era that also have no apparent relation to audio.