Thanks in no small part to the kind folk at M1911.org and my good friend Tam, I managed to fix the problem with my Para P16-40 Limited. It turns that the diagnosis of the leaf spring being slightly out of whack was 100%, and after two tries (and a significant amount of cursing) I managed to get all the parts to line up correctly.
While I was trying to figure things out, probably the most helpful thing I found was this video at the m1911.org site; which shows in glorious 3d the reassembly process for the 1911 pistol.
Honestly, seeing the leaf spring go in correctly in that video (and watching it about 4 times) was a real big help in making sure that all the parts in the gun were aligned correctly. And it still took me two tries, but when I was done, I felt good about it – sense of pride and ownership and all that.