One more thought regarding your allusion toward a psychic factor in antigravity, I feel that is the central factor that throws out current approach off the rails. Consider St Joseph, Saint Teresa of Avila and so many other unnamed folks who knew levitation, especially in the Hindu traditions.
I have little doubt that the spiritual implications (not “religious”) will eventually be found to be of fundamental importance interacting with exotic “psychically” sensitive materials in an intimate fashion to create the “ships”/creatures allowing instant travel without speed of light limitations through space-time.
Having spoken the word “time” I must do a force-stop here and now or I will wander on into outer space!