I'm trying to get the following done:

I've got a source directory S/ and a copy of it in C/.
Every $timespan after syncing S/ and C/ I want to run rsync in such a
way that it copies any changes during $timespan in S/ into a new
directory diff_YYMMDD-hhmmss/ and then updates C/ to be identical to S/.
Newly created files in S/ don't go to the diff_ directory - only to C/.

The result is a bunch of directories diff_... containing ONLY changed files.

I've tried using rsync --compare-dest C/ S/ diff_YYMMDD-hhmmss/ with the
result that both new and existing files are copied to diff_. Adding the
--existing parameter doesn't create anything.

Is there a way of doing what I want?
Please don't recommend rsnapshot. I found that it creates too many hard
links. I also want to avoid changing directory structure (rotating) as
C/ and all diff_s are getting backed up on a tape. Rotating directories
around makes the tape think that everything changed when it didn't and
every incremental backup becomes a full.