Dunno about Vortex, but here's my take on Dialectical-Algorithmic:
It's spaghetti architecture. You have links here, and links there, and it doesn't make much sense and guess what - any single link doesn't really matter. No particular way matters. It's the clusters that matter, where they meet, where they lead... condensation points. But this point doesn't depend on any single link - so the breaking of that, holes in it, don't matter much, it's just one of many. If I were to define DA on my own, I'd say it's about the opposite of relying on any one way, on any line of thought. So there can be no right way, no step by step, no dependable procedure or proof whatsoever. It goes against its nature, which lies in interconnectedness - at the cost of not really creating any stable structure, thus leading to often accurate enough, but not "reliable" results. Or inaccurate, if all the links fail and the redundancy is merely misleading. That's what I think Ganin really describes when he talks about ILIs "circumstantial" or "unpredictable" approach to logic, by the way - Dialectical-Algorithmic style in NT type.
IMO the static system crazedrat described represents Holographic more than any other style, and jughead's rant doesn't rely to any (unsurprisingly).
I suppose Causal-Deterministic compliments it by focusing on building a more stable structure, one that doesn't suffer from DA's main drawback, "so that's more or less somewhere there" tendency. Not quite what jughead describes, anyway.