Ok here are my attempts for more peaceful badges  

The idea of the report system is self cleaning ecosystem so leaves may be good - also easy to recognize for light blue background and to distinguish the class by number of leaves:
300 good reports
1000 good reports
5000 good reports

Or purifying or polishing the forum, for which jewel may suit:
300 good reports
1000 good reports
5000 good reports

Simply report paper:
300 good reports
1000 good reports
5000 good reports

Quill pen to write a lot of reports:
300 good reports
1000 good reports
5000 good reports

Eraser for many rule breaking posts:
300 good reports
1000 good reports
5000 good reports

Simpler form like star would be good as well:
300 good reports
1000 good reports
5000 good reports

Or moon if you do not like star - meaning r.i.p. for many "to the moon" type posts:
300 good reports
1000 good reports
5000 good reports