Thanks for your quick response and for looking into this for me. You're quite right, the UPLOADS constant ends up being prefixed with ABSPATH- that's something I hadn't noticed and unfortunately something I can't change without modifying the core.
A workaround I have now found is to set the UPLOADS constant to “../media”. Although this does generate links like e.g. http://domain.com/../media/mypicture.jpg this is not serious in my case.
You can close this ticket as the issue is now resolved.