I have played this save for a while. Stress was mostly a constant stream downwards into infinite happiness and joy, with the occasional dwarf who is never happy but also never stressed.
Until a siege, at which point most dwarves saw 30 goblin bodies at once and immediately went to positive-stress, one of them gaining over 15000 ("great deal of stress") upon the instant. Precisely one dwarf was already haggard and drawn before this, because he kept seeing a dead body I couldn't find (I had missed some teeth) that nobody else was bothered by.
From what I can tell, the entire reason for the stress issues is lack of dwarven scope insensitivity: in other words, dwarves see 20 dead bodies and are 20 times as bothered by it as if they see one. This is just not realistic behavior.
I should note that I play the game in a very lackadaisical way that, well, if you'll believe it, is far more efficient than the average player, by its very lackadaisical nature. I always approve petitions from entertainers, 100% of the time, because I think it's more interesting to have a lot of them around, and I kinda feel like that might be a reason for me having little-to-no stress before the siege, combined with my spending pretty much all of my labor on luxuries: drink variety, cooking lavish meals, keeping lots of mugs, making instruments, improving the temple and library.
So, my proposed solution is: easier way to dispose of bodies, less multiplication of dead body thoughts.
Needs are a problem, and a pretty big one, but as far as I can tell they're a mostly unrelated problem.