Irrepspective of the amount of negative mass matter required, it's still a fact that these schemes require negative mass matter to work, and negative mass matter is not known to exist. And there are still problems with faster than light travel that you would have to resolve--in particular, that a solution like this would enable you to construct a time machine, and then you'd have to have a way of resolving all of the time travel paradoxes we know and love.
Full disclosure: I am also a former student of Richard Matzner, FWIW. I have never discussed this matter with him.