I don't know if you were already aware of this or not, but the code that runs this echo chamber has been available freely for some time - although it hasn't been updated in some time either. A while back when there was a new beta being forced down our throats here, there was at least one site (soylentnews.org) that built a new site from modifications of the old code. While their community is not as large as the one here, they do cover similar material. More to the point, if you want to try to fund a specific improvement, you might find their crew more receptive than the guys who work on the code here.
They certainly aren't trying to engage in rational conversations
Currently, yes. A large portion of the conservative majority here has no interest in rational conversation; they just like to fling stuff around and see what sticks. However, this is not 4chan or townhall.com; historically slashdot has worked because of the community of users. It really should not be irrational to expect a sincere discussion here ... emphasis (unfortunately) on should.
They are insane (probably sociopaths or pathologically ignorant) or they are paid to act like they are nuts.
I think that depends on how one defines "insane". While we have had people here who fancied themselves "professional trolls" they have grown tired of their own act and left. I think what we're left with aren't necessarily trolls in the strictest sense of the word, I think rather they are people who actually believe what they say and don't give a shit about what anyone else has to say about it. Although if you consider that to be trollish behavior, then that would classify Drumpf as a troll and probably explain a lot.
Where does "profoundly stupid" fit in?
You and I don't have much of a history here, so you probably don't know my experience with that phrase and why I try to avoid it. A certain midwestern governor - who spent over 2 years running for the presidency only to drop out not long after his first Iowa straw poll - labeled a large part of his "home" state population with those exact words for disagreeing with him. I don't expect that you would have been aware of that before writing it but I do occasionally bring up that statement from the guy I call "The Teflon Candidate".
To answer your question though I doubt that truly stupid people would find this site to be worth their effort. While it is more politics - and less tech - than it used to be, it still focuses mostly on content that a lot of people wouldn't want to put time into.
Sincere religious delusions?
Religion and politics have become so intertwined - and indeed for some people indistinguishable - that you could call many of our biggest political parrots here religious zealots.
Or some kind of masochistic pleasure in losing arguments?
I don't think a troll is capable of admitting to ever losing an argument. Come to think of it, a slashdot conservative almost never is either - I suppose that supports your argument some.
Too much thought wasted on the trolls. Or is that their real goal?
I'm quite comfortable in my belief that they do not aspire to drive anyone to think.