It looks like ProgressBar is not available to scripts in DxDesigner unless I am making an error.
Do I have other options in DxDesigner scripts equivalent or similar to the PCB scripting methods Application.GUI.ProgressBar()?
No, DxDesigner does not expose a progress bar like Expedition.
You can write status updates to the output window using Application.AppendOutput.
Alternatively, if you are feeling creative, it is possible to write some fancy html to the output window: