If parsers are a major concern, I'd be down with some sort of personal medal / reward system. Perhaps at the end of each boss in dungeons/raids etc. you are awarded a personal Bronze/Silver/Gold medal based on how well you did for your job (DPS is part of it, but not the only deciding factor.. i.e. points could be awarded for logically using party buffs, utility and support skills, and points could be added for interrupting attacks etc.) Then you receive a reward based on your medal. So, say Silver medals give the current reward, Bronze medals give half tomestones and Gold give double tomestones + gil or something.

That would provide incentive for people to improve, and would not give your numbers (or medal) to other players and thus wouldn't be used to shame you.

To clarify, by logically using party stuff, I mean like a BRD singing Ballad if the healer is low on MP - but would not get points if everyone is at full MP.