[Blood Royal] Mechanics help

I've been redoing the mechanics of Blood Royal, my 24-hour game; the original dice rules were really messed up, something I unfortunately noticed only after publishing. The non-crippled version (I haven't put any of my other changes online) can be found here.

The biggest problem I've run into is that with Blood Royal's stat system, it's hard to come up with a balanced dice mechanic. Currently, there are five stats, each with a score between -6 and 6, and zero as the average. It uses a dice pool (and I want it to stay that way; the "feel" I'm going for is, in a few words, dice chaos), d6s only.

It's pretty simple to test for a positive stat; just roll your pool (in those rules, the size of the pool is equal to your score in the stat, or 1 if the score is zero; I changed that during the still-ongoing playtest to 6d6, no matter what the score), and each die that comes up under the stat is a success. The King (GM) sets a minimum number of successes that must be achieved before the action itself is successful.

But with negative stats, it gets messy. Originally, there was no difference between rolling positive and negative -- only that someone else rolled a negative for you. I like that part, but there should still be some difference as the positive and negative don't represent mirror-images, but a scale centered on an average of zero. And I'm not sure how to get the dice to do what I want... I'm planning to scrap both 'sides' of the system and start from scratch, but I'm not sure how to do that. I like the positive and negative stats, but if I can't find a way to get the dice to work I'll probably end up with a standard 1-whatever scale.

Any ideas?