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.