The RLA is all about having parties work things out between themselves through alternative dispute resolution procedures such as arbitration and mediation without court involvement.
You seem to imply there is some sort of conflict between the RLA and arbitration law here. There isn't. (Or if there is, please explain.) Even of there were, courts generally do what they can to interpret apparently conflicting laws to be in harmony with other as much as possible. They do not choose one and throw out the other if at all possible.
A union has broad powers to negotiate, yes. But not unlimited powers. And the RLA does not require that integrations be done by seniority.
Also, consider laws such as McCaskill-Bond. It has amused me over the years how some East supporters have pointed to that law as proof of how they are right, even though it is essentially a different version the same as that evil and unjust ALPA merger policy. In fact, it was enacted to protect a minority group (there, TW) from tyranny of the majority (AA) during a seniority intergration process (sound familiar?), and limits a union's "broad powers to negotiate." Is it therefore somehow in conflict with the RLA? Does one trump the other?
In any case, I am not really even sure how the RLA is implicated. The RLA addresses disputes between carriers and unions, not inter- or intra-union disputes, which is the underlying issue here. USAirways does not really care what seniority list ends up being used. The only real "negotiating" about seniority that will be going on is between East and West pilots, not between USAPA and USAirways - an situation that is not really addressed by the RLA.

You might want to read the Federal Arbitration Act or google the Steelworkers Trilogy.
How will the integrity of the RLA be compromised if (when) Nic is to be the ultimate list?