What are the state-of-the-art English syntax theories there are that can explain all the English syntax phenomena?

In some way, this question just underscores the fundamental problem with 'syntax' theory. It takes an idealized notion of 'a correct sentence in a language' and tries to come up with formal rules for generating all possible sequences of lexemes in such a way that all correct possible sequences are generated by those rules and no incorrect possible sequences are. The notions of dependency and constituency are just ways of arranging those rules with respect to putative relationships among the words within a correct sentence. But even if they were successful in that (which they aren't) they wouldn't get around the fundamental problem of the consequence of the initial idealization. If you assume the fundamental unit of syntax to be sentence (or even clause), you are mostly limited to written language for your universe of sentences. But even then you have all those 'imperfectly' formed sentences or varying judgements on acceptability among native speakers as to the acceptability of those sentences. In spontaneous speech, you don't even have sentences.

So your next step is to posit an arbitrary distinction between competence and performance and ignore all the aspects of performance. But you then get the problem of bootstrapping your target set of sentences from this imperfect 'real' set of performed sentences, then rejecting them, and defining language only through the rules. Therefore, in a formal (constraint-based) theory of syntax, you can never account for the totality of the syntactic phenomena you encounter in the real world.

The construction grammar framework was explicitly designed to deal with this issue. But it thinks of syntax very differently, so you cannot think of it as a third alternative to dependency or constituency. It simply does not think of sentence or clause structure in terms of heads but rather abstract schemas into which words can fit. So instead of S --> NP VP you get something like The ___ Verbed ____ into a _____. These constructions are considered to be part of an inventory alongside traditional lexemes. This means that you have a lot of 'rules' that are difficult to abstract away into structures (like trees) that are directly translatable into algorithms. Instead, you have to model them as they are. You get a lot more linguistic and cognitive plausibility this way but not a 'grammar' framework that can be evaluated on the same criteria - ie. positing of just the right constraints to produce only acceptable strings (sentences).