Tetrahedral microphone arrays offer a relatively efficient means for virtualization of a loudspeaker in a room. However their first-order Ambisonic room impulse responses (ARIRs) are only poorly resolved, directionally. One would typically desire the directional resolution of third-order ARIRs for binaural or fifth-order ARIRs for loudspeaker-based reproduction. The enhancement or sharpening of the directional resolution from first order to higher orders has recently been done by the Ambisonic Spatial Decomposition Method (ASDM). This contribution proposes a related method that outperforms ASDM. Instead of the pseudo-intensity vector, it uses a dual-direction detector and a 2+2 directional signal estimator that are inspired by the High Angular Plane Wave Expansion (HARPEX). After revising the geometry of the dual-direction signal model, the paper introduces a short-term averaged detector, an optimal complementary direction pair, and a regularized signal estimator. Both estimator and detector are tested in a technical analysis and the paper concludes with a comparative listening experiment indicating the advantage of the new method.