Cannot set vertical datum and other custom parameters for projected CRS data

[Moult]

The UI only supports an EPSG lookup for the CRS name, but oddly enough no EPSG lookup for vertical datum. Why is this the case? Is it possible to use an EPSG lookup for these to prevent user input error? By default, users aren't even aware there is the possibility of a vertical datum to be set since it is hidden in the project shared parameters.