I really have no dog in this fight but it doesn't matter who arbitrated the SLI. It's a freedom-of-contract issue. Both sides signed the contract - agreeing to BINDING arbitration.
It doesn't matter in the least who or what decides the SLI - nor does his/her affiliation. Whether it was a mediator with a bazillion airline cases under his belt, Daffy Duck, an arm wrestling match, poker game, or coin toss, you agreed to the method beforehand. You had a contract.
Now, you think a new mediator is going to just ignore this contract and overlook the previous BINDING arbitration - to which you already agreed?
You guys may have gotten the short end but a contract is a contract. Deal with it.