Good news -- after I declined their settlement, JAMS sent the request for payment of the initial arbitration fees.
I made Midland the settlement offer -- drop your lawsuit, I'll drop arbitration and set the expiration date of my offer the same day the fees made payable to JAMS are due -- and they accepted!
We're going back and forth on the finalization of the settlement offer now, but they agreed to drop everything. I consider this a win!
What you need to do is:
1. Make sure the case is dismissed WITH prejudice.
2. Make sure you and the JDB agree to drop all disputes against each other from the beginning of time until now, or for any action occurring before the signing of the agreement.
Note that this sort of agreement doesn't preclude them from buying another debt, but if you word it properly, if you defaulted on the debt before signing the agreement, this would preclude them from collecting on that debt.
You could try to get them to put in something that they would never sue you for any other debt. They probably wouldn't agree, but they might.