There is nothing said from the Founding Fathers about being a third party mediator, even with troubled Europe and the Far East. Obviously, it was a little more complicated in those times as the world was different and communications took far longer to get hither and dither. But, I don't think being completely reclusive was their intention either. We are a world leader and have been for over a century. I wouldn't think the Founding Fathers would object to this nation, especially in light of how powerful we are, taking a lead role in negotiating a peaceful solution to a problem between two other nations. Especially nations we trade heavily with. The first action is to let the two work it out. But if we must get involved (when we get involved), we do it from the disinterested standpoint.
Regardless, I doubt this will get as crazy as some think. Both countries have far more to lose economically if they start trading serious blows back and forth. And I doubt either one want to risk that with a small strip of land or building a roadway.