This paper proposes a further improved technique on the stochastic functional approach for randomly rough surface scattering. The original improved technique has been established in the previous paper [Waves in Random and Complex Media, vol.19, no.2, pp.181-215, 2009] as a novel numerical-analytical method for a Wiener analysis. By deriving modified hierarchy equations based on the diagonal approximation solution of random wavefields for a TM plane wave incidence or even for a TE plane wave incidence under large roughness, large slope or low grazing incidence, such a further improved technique can provide a large reduction of required computational resources, in comparison with the original improved technique. This paper shows that numerical solutions satisfy the optical theorem with very good accuracy, by using small computational resources.