If nothing else I'd like to think that it should put to rest the notion that I'm a hater who can't tolerate anything beyond the original series.

Particularly during the first half of the series I had quite a bit of fun revisiting these episodes.
When I'm done with TOS and TAS I'm going to revisit the films. Initially I watched the first two and a half seasons of DS9 before I drifted away, and so I'm debating whether I have any real interest to revisit the series. Presently the only memorable and worthy episode I remember from the later seasons is "Beyond The Stars."
I have absolutely zero interest in watching VOY in any capacity. In regard to ENT it isn't wholly impossible that I might one day try getting through it, but there are other non Trek related works I have more interest in first.
Well, here's my two-cents worth: for what it's worth, I believe you
did give TNG a very good chance, and as far as I can tell, you're only largely wrong about season 6, which has a second half far better than you give it credit for. Otherwise, you aren't, in your critical analysis of the show, that far off.
And I will say this: Deep Space Nine is a brilliant show
if you aren't looking for a space adventure. It has a rather poor first season, and that is primarily because it was trying to imitate TNG with their wacky sci-fi plot of the week, and frankly, the DS9 characters just weren't right for that sort of thing, and neither were the DS9 writers.
However, if you open your mind to the possibility that the Star Trek universe and premise can contain a television series that is a character drama based on an exploration of war, religion, politics, and the human condition (an exploration of the human condition far deeper, psychologically, than anything TOS or TNG ever did), then you will fall in love with Deep Space Nine. No, it isn't often mind-expanding science fiction or rollicking adventure. What it is is a complex, layered, and insightful exploration of human beings. It's a character drama, an excellent one. And if you can get yourself into that mindset, with those expectations, then someone with your obviously perceptive critical abilities will, I suspect, begin to really appreciate it.
I may be wrong. But I think you may surprise yourself.
Anyway, as for Voyager, Enterprise, and Star Trek Generations, Insurrection, or Nemesis, I will echo the majority sentiment, and suggest that you don't bother.