So some of my experience:
The Edge was using strats on War, and even before. War wasn't exclusively strats, but I think I can hear the chimey difference on Sunday Bloody Sunday from the fatness of Surrender. Also he has a strat in the video for New Years Day and in the live performances of Under a Blood Red Sky, and I'm guessing he isn't switching from the explorer to the strat just for the live performance.
I've seen The Edge play Rickenbackers, Strats, the Explorer, and Les Pauls and he seems to always sound like The Edge. I'm guessing the guitars (and thus pickups) don't factor into it as much as we think.
On the sound: I ordered those Heradim picks (yes they were $14 shipped, expensive) and ran into a lucky accident. Just by luck, my AC-30 was set to where picking with the Heradim picks clipped the amp just a bit(I was using the normal channel). If I used the smooth side of the picks or my other picks, there was no real clip, but with the bottom end with the rough texture, picking straight down clipped just enough to where my ears went, "that is the sound!".
I threw on some of his classic 3/8's and other delays with my 57' American Hot Rod strat (middle pickup) and nailed his early sound (at least to my ears). The clipping just adds that extra ringing and chime while compressing just enough to ear all of the notes somewhat evenly. My neighbor knocked on my door to compliment the sound, heh. When I turn the volume of the amp down, it is noticeably different and sounds more like all of my past imitations (and is more suitable for the Joshua Tree sound). If I rotate the pick or strike the strings at an angle, it changes the sound (doesn't really clip). Its quite interesting, actually. Muted string strokes sound really cool with the pick, as well.
I'm going to see if I can record this soon and post it. I'd love to get my hands on an Explorer to see if that makes much of a difference.
Intriguing... Let us know what you find out...
I've been using my fingernails for the clipping sound for years...
dm.lj (I write songs--updated 10/8/09)