Well, crap. I think I may have a problem here. It looks like I've done some main plots out of order.
After speaking to Paarthurnax, I headed back down the mountain and talked to Arengir, who directed me to the College of Winterhold. I now have the questline Elder Knowledge, and so I headed to the library and spoke with Urag gro-Shub. Only there was no opportunity to speak with him about the Elder Scrolls. The Quest indicator is still just hanging over his head, but no dice. I completed the College plotline waaaay at the beginning of my game, and now I remember that I already asked Urag about the Elder Scrolls, because it was an option back then. I have no idea what I did with the books he gave me, or if I asked him about them, but I DO remember that I already discovered Septimus Signus' Outpost while swimming around behind the College (it was honestly just something I happened upon, I do not remember any sort of quest indicator). The Attunement Sphere and Black Lexicon have been in my inventory for about 30 hours now. I have the questline "Discerning the Transmudane" open.
So now I'm worried. The Quest for Elder Knowledge still just tells me to go to the College to find out more. Should I just try to do the Discerning the Transmudane quest, or have I epically messed up my game? Should I perhaps try to locate the book Ruminations on the Elder Scrolls and see if that's a fix if I bring it back to Urag? Odds are good it's still somewhere in Whiterun, either at a shop or in my house.
Help!
ETA: Just transcribed the Lexicon and retrieved the Scroll, looks like everything is fine! Phew.