Hot Jupiters present a unique opportunity for measuring how planet formation history shapes present-day atmospheric composition. However, due to the myriad pathways influencing composition, a well-constructed sample of planets is needed to determine whether formation history can be accurately traced back from atmospheric composition. To this end, the BOWIE-ALIGN survey (A spectral Light Investigation into hot gas Giant origiNs by the collaboration of Bristol, Oxford, Warwick, Imperial, Exeter, +) will compare the compositions of eight hot Jupiters around F stars, four with orbits aligned with the stellar rotation axis, and four misaligned. Using the alignment as an indicator for planets that underwent disc migration or high-eccentricity migration, one can determine whether migration history produces notable differences in composition between the two samples of planets. This paper describes the planet formation model that motivates our observing programme. Our model traces the accretion of chemical components from the gas and dust in the disc over a broad parameter space to create a full, unbiased model sample from which we can estimate the range of final atmospheric compositions. For high metallicity atmospheres ($\mathrm{ O}\mathrm{ /H}\ge 10 \times$ solar), the C/O ratios of aligned and misaligned planets diverge, with aligned planets having lower C/O ($\lt 0.25$) due to the accretion of oxygen-rich silicates from the inner disc. However, silicates may rain out instead of releasing their oxygen into the atmosphere. This would significantly increase the C/O of aligned planets (C/O $\gt 0.6$), inverting the trend between the aligned and misaligned planets. Nevertheless, by comparing statistically significant samples of aligned and misaligned planets, we expect atmospheric composition to constrain how planets form.