IMO, they will get the important items to beat the Finn in Caemlyn, namely firesticks & fireworks from Aludra, possibly the music box ter'angreal from Elayne and maybe a cuendillar chain (which is originally of iron). The cheating is that these items don't appear to be forbidden at first sight, but include the forbidden materials to beat the Finn.

Then they will use the fire (firesticks & fireworks) and music (music box ) to blind and daze the Finn. In this moment of confusion, I believe Thom will catch and bind one of the Finn leaders with the cuendillar chain. They can then exchange their prisoner with Moiraine. That would be the perfect turnaround of the rules, since in the game, the Snakes and Foxes try to catch the human piece.

Likely Mat has to sacrifice his left eye before, because it's the link to the Finn and they would otherwise anticipate their plan (Egwene Dreamed: "Mat, placing his own left eye on a balance scale", and the foxhead medallion apparently also only has a left eye).