Context. Early B-type stars are invaluable indicators of elemental abundances of their birth environments. In contrast to the surrounding neutral interstellar matter (ISM) and H ii regions, their chemical composition is unaffected by depletion onto dust grains and the derivation of different abundances from recombination and collisional lines. In combination with ISM or nebular gas-phase abundances, they facilitate the otherwise inaccessible dust-phase composition to be constrained. Aims: We determine precise abundances of C, N, Mg, Ne, and Fe in early B-type stars in the Orion star-forming region to: a) review previous determinations using a self-consistent quantitative spectral analysis based on modern stellar atmospheres and recently updated model atoms; b) complement our previous results for oxygen and silicon; and c) establish an accurate and reliable set of stellar metal abundances to constrain the dust-phase composition of the Orion H ii region. Methods: A detailed, self-consistent spectroscopic study of a sample of 13 narrow-lined B0 V-B2 V stars in Ori OB1 is performed. High-quality spectra obtained with FIES at the NOT are analysed using both a hybrid non-local thermodynamic equilibrium (non-LTE) method (i.e., classical line-blanketed LTE model atmospheres and non-LTE line formation) and line-profile fitting techniques, validating the approach by comparison with previous results obtained using line-blanketed non-LTE model atmospheres and a curve-of-growth analysis. Results: The two independent analysis strategies provide consistent results for basic stellar parameters and the abundances of oxygen and silicon. The extended analysis to C, N, Mg, Ne, and Fe finds a high degree of chemical homogeneity, with the 1σ-scatter typically being 0.03-0.07 dex around the mean for the various elements. The present-day abundances of B-type stars in Ori OB1 are compatible at similar precision with cosmic abundance standard values as recently established from early-type stars in the solar neighbourhood and also with the Sun. Based on observations made with the Nordic Optical Telescope, operated on the island of La Palma jointly by Denmark, Finland, Iceland, Norway, and Sweden, in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias.Appendix is available in electronic form at http://www.aanda.org