Welp, I didn't make it to sleep, but I did solve the final thorny problem of the day related to this server migration. And it justified, at least in the eyes of others, the part of my job description that says I am "the most senior expert on Microsoft SQL Server in the agency." It's bullshit, but for the moment I'm a hero, all things considered. I'll take it.
Now I can stop thinking until 7am.