To get r_s>>l_p I'm just using the classical Schwarzschild relation r_s = 2GE where I have equated the centre of mass energy E with the mass. G is something like G= (l_pl)^2 the planck length squared. So if E>>m_pl=1/l_pl therefore r_s/l_pl = 2E/m_pl>>1.
Clearly it doesn't make sense to associate E with k. E is only the centre of mass energy it doesn't say anything about impact parameter b i.e. how "close" the particles come. Something more like k~ E^c b^-a would make more sense where a and c are positive constants say c=1 b=2(with some approiate power of G to give it the right dimensions).