Abstract One systematic limitation of solar coronal hole (CH) detection at extreme ultraviolet (EUV) wavelengths is the obscuration of dark regions of the corona by brighter structures along the line of sight. Another problem arises when using CHs to compute the Sun’s open magnetic flux, where surface measurements of the radial magnetic field, B r ⊙ , are situated slightly below the effective height of coronal EUV emission. In this paper, we explore these two limitations utilizing a thermodynamic magnetohydrodynamic (MHD) model of the corona for Carrington rotation (CR) 2101, where we generate CH detections from EUV 193 Å images of the corona forward-modeled from the MHD solution, and where the modeled open field is known. We demonstrate a method to combine EUV images into a full Sun map that helps alleviate CH obscuration called the minimum intensity disk merge (MIDM). We also show the variation in measured open flux and CH area that is due to the effective height differences between EUV and B r ⊙ measurements. We then apply the MIDM method to SDO/AIA 193 Å observations from CR 2101, and conduct an analogous analysis. In this case, the MIDM method uses time-varying images, the effects of which are discussed. We show that overall, the MIDM method and an appreciation of the effective height mismatch provide a useful new way to extract a broader view of CHs, especially near the poles. In turn, they enable improved estimates of the open magnetic flux, and help facilitate comparisons between models and observations.