If you are looking for a joiner in Greek, then I'm your man. I shared your frustration about all of the different categories because they can hinder the synthesis of all the different bits into a unified whole. At the end of three years of Greek in seminary I could translate, sight-parse, and give a rough syntactic force (Wallace had not yet been published), but I still didn't feel like I had a good sense of how the language hung together. All the bits remained discrete bits that I couldn't join. I headed into linguistics to see if there was some better way of doing things, and that's where I found a function-based approach to description. The shift from how to translate it to describe what it is doing, why the writer might have used this versus that, revolutionized my thinking.
In my zeal to find something else that was more comprehensible for me I threw out more traditional grammatical descriptions. This was a bad idea. You see, Wallace, Robertson, Blass, Funk, these guys really know their language. The problem is that they lacked a descriptive framework that really fit Greek. They have important insights to offer, but it requires the reader to do the legwork of understanding what they are saying. I have learned a tremendous amount from these scholars, and tried to demonstrate that in each chapter of A Discourse Grammar. I may disagree with some at certain points, but my main beef is with the framework, not their knowledge of Greek.
Lumping will only get you so far. My book presupposes many things, like you understand morph, basic syntax of the clause, etc. When it comes to precision and detail, like the kind that accompanies theological study of grammatical issues, lumping is a poor substitute for precision. I may be a lumper rather than a splitter, but I deeply respect the splitters. They can do things I lack the skills and gifting to pull of. Both serve a purpose, both are needed. If I would want to change one thing, it would be to see more accurate lumping introduced early on. Some of lumping we see in introductory grammars is misleading, but profs expect to correct it in second year when the splitting begins. I think we need to come up with better introductory lumping, the kind that will provide a solid foundation rather than needing to be unlearned in second year.
I do not want to start a pedagogy discussion, too many already. My point is to think about ways of describing grammar and syntax that could be readily understood from the beginning, and that are robust enough to stand the test of lifelong learning.
Do not let your frustration with the splitters lead you to ignore what they have to say. Been there, done that, and I've repented.