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Under the sticky list, there's a thread with the very subtle name, "The Definitive Amex 3X CLI Guide" Wonder if that could be useful here.... Let's see...
American Amex credit limits are capped at 200% increase. Update: Requesting CLI > 3X no longer results in automatic denial. If the account is eligible for CLI, then new limit is counter offered keeping the 200% cap in effect(meaning CLI counter offered will not exceed 3X current limit under any scenario)
I also wouldnt tell them you just opened a number of other cards with higher limits, that is more likely to scare them than help you