What is the source of your GCPs? Offhand I cant think of any reasons why your drone images are placed at different heights. Did you perhaps try adjusting the image properties? Image Properties > Image Options > Adjust Image Altitudes.
It would be useful to know whether the altitude values for each image also show this abrupt change in altitude? This would be easy to see from the image properties pane as in below image. Therefore pointing to whether the problem lies with the recorded altitude metadata values or the Drone2Map/GCP processes.
What makes you think that the two elevation surfaces are not showing up? They are invisible as they are only used to adjust the height of the 2D layer pixels but you can see them if you turn on Shade Relative To Light Position on the Elevation Surface Appearance tab. Or you could try draping over any other raster surface.
Your situation is certainly unusual and I don't think I have any answers but it will be useful to better understand what is going on.