I don't know if this will help, but I eventually managed to upgrade.
There were lots and lots of issues though. It was less than smooth.
First, make really sure that you have easily-restorable backups of your vCenter VM. The update will go wrong a few times!
Starting the upgrade using the installer application from Windows managed to set up the new vCenter appliance but failed to migrate the old.
Connecting to the web interface of the new appliance started the upgrade but the web interface eventually times out and there is apparently no way then to check on the status and/or the process will fail if the interface is timed out. When I got it to work it was wen I kept the interface busy so it wouldn't time out on me. This is particularly annoying.
Unfortunately I don't remember most of the things I did to make it work and how many of them were really necessary or useful and how many were rituals that I would now repeat forever without understanding if I could remember.
The key point here is, I guess, that it will eventually work. It just needs a few tries.
All-in-all VMware upgrade processes remain liquid and what is most annoying is the subtle changes in the user interface which makes it difficult to follow instructions to the letter.
Update: After I typed this and clicked "Post", the web site forwarded me to the login page. Luckily the text was then posted when I logged in. But I guess if the logon had failed, it would have been lost. Awful experience with the web forum, it really is.