I remember seeing a chart showing that it was possible to reach other stars using a technique like this. Unfortunately the problem is slowing down.
So this is like being concerned how you will spend all that money, once you make it :-)
There's a lot of discussion on interestellar travel, but "we" have almost frozen solar system travel. Yes, there are very nice probes out there doing important work, but manned vehicles are limited to keep ISS's lights on.
The "impossible" tech needed to reach the stars will most probably be discovered or refined while conquering the solar system.
Big sailing ships were developed along four centuries of sailing. The analogy may not be perfect, but I think it's eye opening.