negative Hubble-constant

Imagine the Universe was contracting and the Hubble-constant negative (with our current definition as the distance-normalised recession velocity): What interpretation would the scales \(c/H_0\), \(1/H_0\) and \(\rho_\mathrm{crit}=3H_0^2/(8\pi G)\) have? Would they be sensible scales? Would the scale be independent, and why is \(c/H_0\) so close to \(c/\sqrt{\Lambda}\)?