The TAS reference is not dated, nor associated with any particular species or culture; it could apply to an ancient discovery that resulted in the first AG technology known to the TAS-era UFP member species, some five thousand years before the UFP was even founded.
Agreed to a point. From my own vantage point, I have arbitrarily selected 1974 as the date things happen in favor of AG systems. The events of the "McKinley Rocket Base Incident" aka "Assignment Earth (TOS)" clearly places the events of TOS/TAS in an alternate timeline. We know that this incident prevented a nuclear exchange on Earth at least prior to the Eugenics Wars. I believe this period of peace allowed amazing technologies to be either harvested from near-Earth sources or developed planetside outright. I also believe that there was a robust post-Apollo space race which occurred (with all 20 Apollo missions planned and executed successfully.) I do not believe Star Trek's future history as suggested in TOS/TAS runs at all parallel with our own timeline in general. Clearly we did not experience the 'last so-called world war' in the 1990s, there are no eugenics supermen loose among us, and there are certainly no advanced interplanetary vehicles present in any nation's inventory. One can only conclude that what we see on-screen took place in an alternate timeline.
We know advanced AG tech was found down on Earth by Henry Starling in the 1960s, as per "Future's End". We never saw the tech applied by Starling, but for all we know, the AG systems on the Botany Bay were manufactured by Starling's Chronowerx, and need not have been the first of their kind, even.
Having reviewed the episode in question and having consulted the usual standard sources on this episode, one can only conclude that this incident also occurs in in it's own subjective timeline, with Starling's exploits being resolved with a single torpedo strike at the end of the episode. That is not to say however that some sort of similar tech revolution occurred within the context of TOS/TAS which allowed for the application of the systems in question. In my mind, you would have to have some form of advanced onboard computer system that would monitor and execute commands related to ship's AG/Inertial Dampening systems. All we heard from onscreen evidences, is that
Botany Bay had old-style atomic power and transistor units, but that listing of onboard systems was abstract in form and not at all complete.
Perhaps Khan and his super-friends were primarily created to do super-science, and invented AG for their respective patrons all across the globe roughly at the same time? Perhaps lesser, "ordinary" scientists did that, possibly back in the forties already?
I rather like this idea. Khan's age as a baseline would seem to fit for a pre-1980s bit of technical wizardly, assuming he was born around 1959 (As even Into Darkness suggests for it's own purposes).
But if the technology really was natively developed, I'd expect spinoffs and applications, and we see none in the 1960s, 80s and 90s visits to planet Earth. Or in the 2010s visit of "Past Tense", for that matter! Also, shipboard AG seems to be unreliable, limited or limiting in the 2030s still, as it's turned off aboard Ares IV in "One Small Step"... Then again, the propulsive prowess of that class of vessel (rescue mission was indicated to reach Mars from Earth in less than a week!) does suggest application of AG technology. All this in mind, I personally favor the idea of Starling peddling his poorly understood future tech for applications not much unlike DY-100.
Call me narrow and biased, but for the sake of this discussion, I will go on record as saying that my preferences for on-screen evidence lies between TOS and the very extreme, TUC. Once one partakes in what the TNG+ period has to offer as far as technical continuity, I believe we quickly begin to see a definite point of departure between the era of TOS/TAS (Third world war in the 90s, Humanity avoided a costly nuclear exchange etc) and TNG and it's companion spinoffs (No Eugenics wars clearly dated or referenced aside from onscreen "easter-eggs", vehicles with absolutely no AG onscreen until "First Contact", WWIII in 2053 with a post-atomic horror etc.). I wish I could say that being inclusive of these two points of departure together would be productive for this discussion, but I cannot honestly say that even after all of this time being a fan. The two just do not jibe without the TOS/TAS era being shoe-horned to fit TNG+. In my mind, this should be the other way round, but that is a whole other argument, and one that has probably been beaten to death in this forum.
Whether that future tech was Slaver in origin, we don't know - time loops are weird enough that the tech might not even have an origin. But I'd like to think that the TAS discovery features into this somehow. Perhaps it being "the key" should be taken more literally than we have so far though? Perhaps the Slaver flying belt unlocked the mystery of Starling's AG technology?
I do like your notion that perhaps the 'flying belt' was the last key in a very long puzzle which began in Earth sciences. I have no issue with proceeding with this frame of mind. The internet is replete with claims of AG generators and gravitomagnetism. Why not make the flying belt the key which unlocks all of that "hokum"?