I did check "Sleeping in Airports" (and have used it before for other overnight stays), but didn't see anything about TSA times on it.
There's a 1am redeye that I could try to standby on instead, although I'd have to get something from the airline pre-security to show that I'm trying to standby on that, I assume?
Otherwise, yeah, I'll find a place to hunker down pre-security.