Part of the idea with The Project was to use materials and technologies that we know exist now, not to project so far ahead that anything is usable and therefore placing the whole idea into fantasy.

The same thing was done by the British Interplanetary Society (BIS) with the Daedalus interstellar probe in 1970s. One result was having the project taken a lot more seriously by scientists and space engineers than it might otherwise have been.

As I have said before, and if you read in the slide presentation previously posted (the URL), The Project is about a common goal for humanity first for our betterment, interstellar exploration and ETI contact is secondary to the plan.