Back to your question about other ideas - I have thrown a few at Johnny before. My best idea would be granting some sort of pass once/round to certain factions. I see that as a band-aid, not a real fix though. It makes the problem that exists be diminished, but creates its own problems.
In general, I think it is better to address the problem card/rule than it is to try to make it less relevant somehow, since it introduces a new issue. Its like If a single house on my street is bringing down property values. We can fix the house in question or try to cover it with a nice-looking tarp/fence. Both might bring up the property values but one solves the problem and the other just covers it up so people don't see it as much.
Not the greatest analogy, but you get the idea.