How can I rotate many log files into a different subdirectory per rotation?

You should be able to call an external script in the postrotate directive:

postrotate
  /path/to/your.sh
endscript

and have that script do the moving, e.g.:

#!/bin/bash

newdir=/var/log/example/`date +%Y%m%d`

mkdir $newdir
mv /var/log/example.1.gz $newdir

find /var/log/example -mindepth 1 -maxdepth 1 -mtime +7 \
  -type d -print0 | xargs -0 rm -rf

However, it might be easier to just use the dateext directive. With that the rotated files will be appended with a timestamp (although not moved to a different directory).

See logrotate(8) for details about both directives.