When I got back, after talking to Parthurnaax (err, sorry if I mispelled that), I went back to the Blades to talk to Esbern, and he insists I kill Parthurnaax. I'm not ready to do that yet (my character feels that if P is leaving humans in Peace, I'll leave him in peace for now).
I tried talking to the Greybeards and telling Arnguir (again, not sure of the spelling atm) that I wouldn't kill P., but that doesn't seem to be offering me any path forward, story-wise.
If I want to continue the story, is killing P. really my only option? Wouldn't surprise me too much - an aweful lot of the quest arcs are very much "on rails" in terms of not giving you reasonable additional options. For one thing, as Dragonborn, shouldn't I be the head of the Blades? Who are they to tell me what to do? The Aedra, or Fate, or the $60 I paid to Bethesda made me the Dragonborn, so it's been given to me to take responsibility for killing or not killing dragons.
Right now, I'm just trying to collect the rest of the Words, thinking maybe Arnguir will offer me additional options once I've gotten all the words?