We report new experimental results obtained on three different laser facilities that show directed laser-driven relativistic electron-positron jets with up to 30 times larger yields than previously obtained and a quadratic (~ E^2) dependence of the positron yield on the laser energy. This favorable scaling stems from a combination of higher energy electrons due to increased laser intensity and the recirculation of MeV electrons in the mm-thick target. Based on this scaling, first principles simulations predict the possibility of using such electron-positron jets, produced at upcoming high-energy laser facilities, to probe the physics of relativistic collisionless shocks in the laboratory. ; Comment: 10 pages, 3 figures. Accepted to be published on Physical Review Letters on April 23, 2015