I sent my pre-written acceptance note.
My academic influences --- my father, a couple of my friends --- kept reminding me that I should think about which position would yield the best job afterwards. And the place with the nebulous research still hadn't written back, so I have no idea what I could have done there. I'm sure it would have worked out, somehow, but I have no idea whether the research I would have produced would have been sufficient quality to go to the next step. I had to send something before Monday or that would have been too much delay. So I really had only one choice unless I was willing to scrap everything and wait for new answers from other jobs.
(For all I know since it's been 5 days since I last communicated with them --- they were sending me relevant background research I should read --- they gave the job away since I was sitting on it so long. Part of me hopes that they did. Though I know that they didn't.)
The advantage of going somewhere where I don't have any friends is that I can totally reinvent myself.
Green mohawk, here I come!