I published my question as *not* a support question, so no surprise that nobody answered. ??
I’ve been brave enough to solve the problem by myself: the php configuration on the Internet installation was missing a statement about the temp directory, which php uses for uploads. I made a virtual host in the Apache configuration and added a ‘php_admin_value’ directive, for that site, to set a valid temp dir. With an ftp client I made it writable. Then I restarted Apache, just to be sure about the directive becoming active.
Immediately phpinfo showed the updated value for the temp directory.
I logged in to Wp and, guess what, files uploaded with the built-in uploader does not become ghosts anymore. Photopress does not complain anymore about the temp directory being not writable.
Hope this helps someone else solve such a problem without losing as much time as I did!