In the meantime I found another solution, not as elegant as the above:
If there is a Gnome Panel applet that you absolutely must use and it isn't feasible to get an indicator to replace it, then this might be a workaround:
(see Can I use GNOME applets in Unity?)
Then I added xcfe4-panel and gbirthday to the startup applications.
After restart: I chose to get an empty panel, added the notification area to the panel and set it to Auto-hide. Afterwards arranged the panel in such a way as to not bother other parts of your system, i.e in the lower-right corner.
This worked for me although I hope the workaround from Omegamormegil will for me as well.