I am nowhere near being C++ enabled, but on Archicad side I suspect the problem may be somewhere on an elevated level. Each property, which is not set, has the <not defined> default value status. You'll need to find a path to switch this status from "Undefined" to "Value" first. But I have no clue as to how this can be triggered. A screenshot of Property Manager for better explanation of the mentioned "elevated" level:
But in the first two of your screenshots it seems like you have managed to switch this status (API_PropertyCustomDefinitionType?), only the value remains in a <not defined> state.
Archicad 4.55 - 25 | HP Z840 | 2× E5-2643 v4 | 64 GB RAM | Nvidia Quadro M5000 @ Windows 10 Pro x64