I believe the quality of the mechanism matters a little, but not a lot, and that fewer discs per trap means lower chances of jamming.
I'm sorry, but I've started to notice that EVERYTHING you say is wrong.
We don't know how mechanism quality matters with stonefall traps, namely because a trap loaded with slade will still cause minor bruising, no one uses them. For weapon traps, it's extremely well known that the quality of the mechanism has the same effect as the skill level of a dwarf, namely determining the accuracy and the lethality. A non quality mechanism will cause many attacks to bruise or cut, if it even hits, but a masterwork mechanism will regularly cause severs and head-lops and be extremely lethal in general.
As for jamming, it's generally accepted that 1 disk per trap is the best way to go, assuming you have the spare mechanisms. That way, if one jams, there's 9 more that can still fire, and you can get the same slashing power over a greater distance. If space or number of mechanisms is an issue, it's still better to go as loose and spread-out as possible, for the same reason. And, as stated, it appears to be mostly based on the kill shot. Hitting an artery and having the goblin bleed to death atop the weapon trap doesn't jam it, but crushing the skull is more likely to jam because that's an insta-kill. There's also untested evidence that the type of weapon matters, with spears/menacing spikes jamming often and hammers almost never. It seems that in general, the more "skewer on a stick" the weapon is, the more likely it is to jam.