I just own one of the BV perforated but have seen about 10 of them in person and they were all 8'-6, and all the old BV advertising materials I have seen don't mention anything smaller than that.
There was mention of some solid 9'-6" reflectors (I have seen just one of those), not sure if there was a 9'-6" perf reflector offered.
Your 1st measurement method was correct (don't want to measure the curve distance), may have a rare Bird there!
There's people here that have forgotten more about these BV dishes than I will ever know (possibly an ex-dealer or 2?), maybe they can shed some light on the 7'-6" size.
Size does matter, and 7.5' is a little small for some of the signals that are up there but your setup would be a nice "starter" dish for someone, and it appears you have the standard BV H-H mount that one of their bigger reflectors would bolt right onto.
For such a big company BITD there doesn't seem to be a whole lot of info on them, I wish an "insider" would write a book on the Birdview saga.
As far as the missing control box goes that is not a big deal, most people would convert the dish movement control to a modern solution anyway (Titanium ASC1 for example), and a new receiver is required as analog is pretty much obsolete and gone.
Thanks for posting it here and good luck.