First, saying that spacetime, considered as a 4-d hypersurface, has "two sides with two metrics" won't work. The metric of one side fully determines the metric of the other side since both sides belong to the same surface. That's why spacetime in standard Einstein GR only has one metric (which, btw, does not mean that spacetime in standard GR has only one "side", as the article claims). Two different metrics would have to describe two different, disjoint surfaces, which would have no connection to each other, which would mean the second one, being unobservable, would be scraped right off the model by Occam's razor.
Second, saying that negative mass would induce "opposite curvatures" as compared to positive mass, in the same spacetime, won't work. One spacetime can only have one curvature at any given ponit. Considering the simpler example of a 2-d surface should make this intuitively obvious--the same surface can't have two different curvatures at the same point.