I may be out of line, but how about going to the extreme and reconfiguring the software so that only good rep can be given. Some reasons:
1-This way, there is only positive reinforcement among the board members.
2-If anyone has anything to say about you in contrast to your opinion, they can either post on the board, or in a PM (which takes a more serious commitment than giving anonymous bad rep).
3-The outcome will be virtually the same as it is now, minus the hurt feelings. If you see someone with a high "rep status" you'll know that this person has been a positive influence on the board.
4-Bad rep points don't affect the point total anyway. These people usually have a rep power of 1 so if you get a bad rep, post something intelligent and you'll make it back.
5-Bad rep only flames people, causes entire threads where a lot of people vent about the idiots that give anonymous bad rep. And these idiots don't really get their point across, they just make others upset.
I don't know if this is a good idea, but it's an idea I put some thought into so I had to post it and see what others thought. Maybe good rep is best along with the bad rep. It's just not being used in a mature way as I'm sure it was intended. It's just some nutless attention whores going around neg-repping and waiting for a thread to pop up about them. That's their satisfaction.
The rep power is supposed to be for positive contributors, but it looks like it's the negative contributors that have the power.