Well I don't get explicit error. The sub control doesn't seem to be recognized UNLESS the pane is tab with other panes (see my video below).
I tried to do what is proposed in your link, but setting the MaxLevelsForItemContainer to a big number doesn't help.
Also I try to see if inspect.exe would recognize the control and this tool works properly.
I don't know what else I can try. It doesn't seem to be a avalondock bug but im not sure.
I have create an issue just so that I can attached my demo video:
Edit: I found someone talking about the template that could be in cause (maybe this may help?)
Edit #2: I found that if I use the avalondock ExpressionDarkTheme or ExpressionLightTheme then it works fine. All the other doesn't work