It would help if I reproduce the complete question here:
...is there a way to realize the traditionalist respect for the four madhahib and extend it to a legal framework that takes into account newer, serious developments in Islamic law and theology, including more modernist perspectives, Wahhabist perspectives, etc.
The question in a way presumes that the four orthodox legal schools derive their respect directly due to the legal consistency and historical strength of arguments behind their methodology. That may be true for a theoretic sake of traditionalist's argument but historically speaking, people started practicing according to these four interpretations because of administrative reasons and by virtue of their being located in a particular setting where a methodology was formed up, evolved and subsequently presented later foundation for legal corpus. Thus for the sake of precision, it would be more accurate to say that development and evolution of fiqh (Islamic Jurisprudence) came about historically through conflicts rather than being a product of objective and tangible methods.
The realization (above) though elusive brings along a lot of theoretical baggage. A rather concrete point that can follow from this is that the jurisprudential sources of one legal school are no more an intellectual property of jurists of that school. Therefore a jurist of sub-continent may consider (and will certainly be compelled to do so in future) Asad bin Furaat's Mudawanaa, Shafii's Kitab al-Umm and Ibn Qudama's al-Mughanni as much a jurisprudential source as he considers any of the texts/commentaries of Hanafi school of law. I do have a fair idea of the magnitutde of intircacies invloved in exercising jurisprudential preference (Tarjih) and alleged lack of consistency in method if jurists move out of their respective methodologies but what I am suggesting here is not simply a wild game of pick and choose rather an originating mindset that juridic literature would be taken as a whole in times to come due to various inevitable and practical reasons.
I mean how can one neglect encyclopedic efforts like al-Muhalla of Ibn Hazm and Fatawa of Ibn Taymiah just because their respective schools were not developed, evolved and sustained the test of time or seen as a digression from the content of four schools. The degree of depth in Islamic legal methodology and the number of dimensions in which it provides foundational sources cannot be ascertained completely unless the complete Islamic legal material would be taken as a whole and studied as such.
I contend this because the development of any modern Islamic legal system (encompassing all the modern facets of law and not just the quantity of water one should consume when doing ablution - though latter can be a good ethical source for guiding regulatory laws of our modern day consumption habits) cannot remain bounded in a particular school's legal framework and would tend to build upon the collective fabric of Islam's legal base. This development would again be historical due to inevitable circumstances rather than a composed and objective deliberate effort. The signs of such developments are already obvious in the fiqh of trade, commerce and banking and the current period may be understood and remembered in history as formative phase in the development of a Cosmopolitan Fiqh . There is no particular way to imbibe this realization purposefully as it is already being insinuated through various intangible agents. However future historian's analysis would bring about the true character of this formation.
1. I came across this pithy term in transcribed lectures of Dr. Mahmood Ahmed Ghazi on various dimensions of fiqh.