Coronal holes (CH) are dark areas in EUV images that are generally associated with open magnetic field regions on the Sun. CHs detected over the entire Sun can be used to estimate the open magnetic flux in the heliosphere by overlaying them on magnetic field measurements. Making accurate estimates is difficult due to many factors, including limited instrument coverage, uncertainties in the observations, and challenges in reliable detection of CH boundaries. One such CH detection challenge stems from the fact that EUV line-of-sight observations essentially flatten the three-dimensional structure in the low corona, which can cause nearby bright structures to obstruct CHs. Here we introduce a mitigation strategy for avoiding the effects of CH obscuration. Using a global thermodynamic MHD model of the corona, we first generate synthetic EUV images for a multitude of observer locations (chosen to mimic the view of SDO over the solar rotation) and combine them into a full-Sun synoptic EUV map. A CH map is then extracted using an established detection algorithm. The resulting open flux estimates are computed and compared to the model’s true open flux. The mitigation strategy (called “minimum intensity disk merge (MIDM)”) is applied by changing the way multiple EUV disk images are combined. Instead of using central strips, full disk images are used by taking the minimum intensity in all overlapping regions. This allows any CH area observed at any vantage point to be seen in the final map. We compare the resulting open flux and CH areas to those using the standard synoptic method. We apply the MIDM method to SDO AIA 193 observational data for the same rotation, and the resulting EUV and CH maps (with corresponding open flux estimates) are compared. Issues such as CH evolution over the rotation, and synchronizing the effective EUV image height to the height of the magnetic field values are discussed.