The Maps Made Easy GCP system was designed for users of non-geotagging cameras to get it to a respectable amount of precision, as opposed to not be referenced at all. You cannot expect to get point for point accuracy out of 3 GCPs. This work is better done in an offline setting with the finished outputs from Maps Made Easy due to the number of points that are usually needed for quality results.
The GCPs in our system are not used to stretch the imagery as it is reconstructed. Instead, the 3 GCP pair locations (Anchor Points) are used to "set the table" for the rotation and location of the reconstructed surface. None will line up exactly. The error to the locations is minimized based solely on the image based reconstruction.
If you have solid waypoint, the best way to get those points to line up exactly is by manually georeferencing the GeoTiff in QGIS using a Thin Plate Spline deformation model to stretch the GCP locations to their proper coordinates. This is not done by Maps Made Easy.