Replying to myself ;-)
I switched to my admin account, set
the cpanplus-directory to /Users/Shared/cpanplus, had some of the same trouble (permissions etc.),
but there a chmod -R a+w was nearly enough. HTML::HeadParser
still did not install (the install hung after the question whether to
decode Unicode-entities or not), I installed afterwards from the
CPANPLUS/shell, there it worked. It seems that I have to install
the modules as the admin-user.
If someone has a solution for the original problem: It is still appreciated.