I believe that astonishing progress will come from a new paradigm. It might be that just as Newton spent two years away from school because of a plague, that now, too, perhaps some future innovation is forming in the mind of a brilliant youngster who has been freed from school.
There are so many examples from history of people attempting innovations by copying the past only to have them swept aside by a new perception of the problem and therefore its solution.
To give a mundane example, I have on my blog two essays about The Pencil: A History of Design and Circumstance by Henry Petroski (Alfred A. Knopf, 1990). The work is a paean to engineering with the pencil as its metonym. Petroski explains (on pages 223-225) that engineers often were trained to draw by copying architectural treatments. As a consequence much Victrorian machinery has flourishes from Corinthian pillars and similar elements that serve no function.
So, too, with space travel. Chemical engines, nuclear power, solar sails, ram scoops they all may see some applications as we push out into the solar system and then edge out a bit beyond. Nonetheless, it seems to me from history that the solution we seek will derive from a radical perception, perhaps with new senses.
I say that because, in particular, if you went back to 1821, you would have a hard time talking to them about amateur radio astronomy and the markets for amateur spectroscopy.