We show that every positive representation of a free group into SO(2n,2n-1) admits R^{4n-1}-valued cocycles giving rise to proper affine actions on affine (4n-1)-space. We can explicitly find such deformations using generalized infinitesimal strip deformations inspired by the work of Danciger-Gueritaud-Kassel. We also exhibit a fundamental domain for such a proper action bounded by crooked hyperplanes. This is joint work with Jean-Philippe Burelle.