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How would you stop this from degenerating into a lawyer system? Rationality is only a tool. The hired guns will use their master rationalist skills to argue for the side that hired them.
Technically, you cannot rationally argue for anything.
I suppose you could use master rationalist skillz to answer the question "What will persuade person X?" but this relies on person X being persuadable by the best arguer rather than the best facts, which is not itself a characteristic of master rationalists.
The more the evidence itself leans, the more likely it is that a reasonably rational arbiter and a reasonably skillful evidence-collecter-and-presenter working on the side of truth, cannot be defeated by a much more skillful and highly-paid arguer on the side of falsity.