You can show the mediator what was already agreed upon.
Once you reject a TA, it's no longer "agreed upon."
Why would they send something worse to the pilot group just to get voted down a second time?
You're not listening. They won't be sending anything to the pilot group to get voted down a second time, because they'll be able to stall for 5+ years in Section 6 because you'll have no leverage of a strike. After those 5+ years, you'll end up caving on PBS, probably to terms far less than what you've got in this current PBS TA, because the NMB will make it very clear that you're never getting released as long as you hold out for something better on PBS.
You probably weren't in the industry at the time, but a story from ExpressJet's last contract negotiations may help you understand how this process really works:
Back in 2003, the ExressJet pilots were in Section 6 trying to hammer out a deal. This was before Comair and everyone else took big concessions in bankruptcy, so the old Comair rates were still in effect. So, the ExpressJet pilots wanted to improve upon the Comair contract and "jack up the house." They wanted a mid-seniority Captain to be able to make $100k per year. They got down to almost everything in the contract being finished except for compensation.
What did the NMB say to them about their pay rate demands? This is a direct quote: "Come back to us when you've stopped smoking crack."
Less than a year later, the ExpressJet pilots settled for the pay rates you see in their contract today, which is
far below what they were demanding. The moral of the story? You have to play the game, and the NMB makes the rules. What you have in front of you for the PBS TA is the best thing you're going to see, because you're going to get raped in Section 6 if you don't already have a favorable PBS system in place. Don't lose just because you don't know the rules of the game.