I added a couple of new weight exercises to my chest/back/shoulder workout last night - I put in two exercises designed to specifically target my rotator cuff muscles. I am now more confident that it was my rotator cuffs that I injured - at the end of the workout I had two "layers" of soreness in that area - the light twinge of the injury (I took the weight up slightly to see if the shoulder would twinge - it did. Still well below my "normal" weight though), and the good soreness that comes when I work a muscle properly.
So my new theory on my injury is that a big part of it is that while I increased weight on various exercises, I wasn't doing much to work the rotator cuff, which otherwise only gets hit during the initial lift on certain exercises. Eventually, I went too far, and that put too much strain on that muscle. At the least, it explains why I keep overstraining it. This theory is strongly influenced by the parts in "Weight Training for Dummies" that warns of just this possibility. That I have waited this long to do anything about it clearly suggests that I have been using the right book.
If nothing else, strengthening the muscle should make it less likely for me to aggravate the injury again, I hope.