just a suggestion. maybe just leave everything is wgs84. And any markers be in same, and use ellipsoid heights and not ortho heights. Then you don't need to bother with any geoid.
Then bring that data (whatever you use from metashape - ortho-mosaic, or point cloud, or dem, whatever) into Global Mapper. Then in Globla Mapper change the projection to whatever you want. The vertical will still be ellipsoid. You can then load the geoid in as a surface. And combine your surface with it, surface plus surface and you will get the geoid adjusted elevations.
no reason to insist on specific coordinate systems in metashape - most of the time - in my opinion.