Hello wildtypitch,
Seems that in PhotoScan Pro 1.4.4 there's an issue that affects proper utilization of 7405 coordinate system, even with geoid model downloaded.
You can try to use Metashape Pro pre-release version (while we are preparing 1.4.5 update with bug-fixes):
- download OSGM15 geoid model (EPSG::5101) and put it to /geoids/ directory in Metashape Pro installation folder,
- run Metashape Pro and open your project,
- select EPSG::7405 for export.