"It is strange, and not a little sad, that after nearly two centuries of discussion there should as yet be no general agreement among textual critics on the fundamental principles or even methods of their science."
- Hastings Dictionary of the Bible
I think its a given that there is no agreement on methodology, because what methodology that has been applied is simply not up to current scientific standards, even in the fields of historical research.
This can and will only be solved by the invention of a more reliable and scientific method, and a clinching demonstration of its validity.
But even that will make no difference, unless key political components of the current impasse are not addressed, namely, what are the ideological reasons for the division, and what can be done to remove them?