This is new to us and these boards have been invaluable. Here is my experience. Hope it helps you too!
We had 2 accounts with Amex, one blue and one platinum. We quit making payments on one in Sept 2011 & the other in October 2011. We contacted Amex at that time on both accts to see about hardship and were told that they could not do anything until January and to call back then.
In late December, we received a call and both accts had been forwarded to Zwicker. I was able to get on a hardship repayment plan on the Blue account with Zwicker - manageable payments on Amex site, 0% interest, yada yada yada, but the platinum had a much larger balance. They initially offered a 60% settlement. I said I would think it over and call back. Called back the next day with counter-offer of 50%, they said they needed hardship letter and would take to Amex, but doubted Amex would take it. This was on a Friday. Early Monday morning I faxed hardship letter to Zwicker. That night I received call from Nationwide. Over the weekend sometime, this account was pulled from Zwicker and send to Nationwide. They were very nice (can't believe I'm saying that, but so easy to deal with.) I explained situation and counter-offer. They came back with a 40% settlement offer with payments over 2 months. We took it!
Later that same night, I received another call from Zwicker - the agent was very upset that the account had been pulled and said he was going to try and get it back. I was very concerned about this because we had already agreed on a settlement with Nationwide and I didn't want that messed up. I told him to leave the account alone and I haven't heard back.
We ended up paying in one payment, have confirmed receipt with both Amex & Nationwide and received confirmation letter of settlement complete this week.
I have to say that we never thought we'd be in this boat, have managed to pay all cc's without issue. Amex just got out of control. We tried to be proactive, but they wouldn't help. I've heard so many horror stories about CA, but this one was very easy to deal with. I was very skeptical throughout the process, but all seems to have been OK.
Good Luck!