But from where could have Cochrane sourced the astronomical (by today's standards) quantities of anti-matter he required for the project if such is the case? That shantytown where he was building the Phoenix didn't exactly strike me as a place which would be equipped with its own dedicated Fermilab-like particle collider.
If people of his era really had mastered gravity and inertia, it sounds likely that there would be a shining white Mr Fusion appliance in every kitchen - and an antimatter generator for every forward airstrip, ready to supply the tactical aircraft on their sorties against hovertank formations.
Frankly, I see nothing wrong with the "mad scientist launches his own rocket" idea in the Star Trek 2060s timeframe. It would be a bit implausible in our
2060s, or in the Trek 1990s, but not really for a culture that has mastered interplanetary travel in the 1990s and gone secretly interstellar with that tech soon thereafter.