How to set layer elevation on-the-ground in python script?
You might be (should be?) able to achieve this using Python CIM access. Read this carefully: Python CIM access—ArcPy | Documentation
In the tips section of that documentation it basically says that if you're not sure what property you need to be modifying in the cim, change it in the UI and compare with changes in the output json. So I did a quick experiment (though looking back, I'm doing this in a Map rather than a Scene - hopefully the process would work for you).
When my layer's Elevation is set to "On the ground"
I export a layer file to get the .json and open that in Notepad++.
I see
And I can see that the Ground surface for the map uses the same. So it’s tying the layer’s elevation to the map’s ground elevation surface.
Maybe you could do the same with the layers in your Scene to understand how the Ground setting is structured in the json and then use Python CIM access to get the definition, make modifications, and set the definition. Again, heed the caution noted in the documentation:)
Also, here are some examples for common requests using the CIM access through Python: https://www.arcgis.com/home/item.html?id=8772f61319584882bb697ba003030636
Well, CIM did the trick. So many thanks, Kory!
At first I did look it like a year ago also but I did not understand that it is possible to add new properties with setDefiniton method. Anyhow works now like a charm. 
I will add the code over here if anyone will need a hint or smthng.
