It may be while you wait (with nothing to do 
) you could try implementing a custom EDID file for loading via kernel command line as a workaround to light up the external with doc and old laptop, so that it can remain a fully functional backup after the new arrives. It’s not something I’ve ever done, but I’ve seen discussions about it more than a few times on the WWW, such as here.
Have you tried connecting the dock to a TV or some other monitor instead of your customary external monitor, to see if your external is where the shortcoming lies?