My guild does something I hadn't seen before to keep it very random. We run "Champ" tags for the first 24 hrs. With that we set a tag of "Tusken" or "Ewok" for example, then you get to take 1 toon from that tag in and do as much damage as you like. Then when full combat opens up everyone has a starting score. Also, if you win a raid you sit the next one. You get to post a zero but no attacks.
Seems to be working well for us.
EDIT: in the tags, we don't allow toons that can clear to be used...CLS, JTR..etc.