Various unification schemes interpret the complex phenomenology of quasars and luminous active galactic nuclei (AGN) in terms of a simple picture involving a central black hole, an accretion disc and an associated outflow. Here, we continue our tests of this paradigm by comparing quasar spectra to synthetic spectra of biconical disc wind models, produced with our state-of-the-art Monte Carlo radiative transfer code. Previously, we have shown that we could produce synthetic spectra resembling those of observed broad absorption line (BAL) quasars, but only if the X-ray luminosity was limited to $1043$ erg s$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$. Here, we introduce a simple treatment of clumping, and find that a filling factor of $\sim 0.01$ moderates the ionization state sufficiently for BAL features to form in the rest-frame UV at more realistic X-ray luminosities. Our fiducial model shows good agreement with AGN X-ray properties and the wind produces strong line emission in, e.g., Ly \alpha\ and CIV 1550\AA\ at low inclinations. At high inclinations, the spectra possess prominent LoBAL features. Despite these successes, we cannot reproduce all emission lines seen in quasar spectra with the correct equivalent-width ratios, and we find an angular dependence of emission-line equivalent width despite the similarities in the observed emission line properties of BAL and non-BAL quasars. Overall, our work suggests that biconical winds can reproduce much of the qualitative behaviour expected from a unified model, but we cannot yet provide quantitative matches with quasar properties at all viewing angles. Whether disc winds can successfully unify quasars is therefore still an open question.