Bevel on a hole inside of a cylinder

@Box, this looks like what I want, but I can’t figure out what did you do to get from left model to the right one. Here is what I have, I mean I can delete the double tube and have my hole through, perfect circle around it on a surface of the curved cone, but I don’t know how to create the bevel from here.

I’ve tried to scale the tube, but I’m getting pretty nasty artefacts. Bottom radius is ~2000mm, so there shouldn’t be any round errors.