Is anyone having the "Cannot copy SteamNew.exe to Steam.exe" problem on Steam?
I discovered Steam's "Repair tool" in the installer. I'm not sure if it matters, but during my earlier troubleshooting, I deleted everything in my Steam folder except for steamapps, userdata, and "Steam".
The Repair tool ran for quite a while (it seemed to be stuck at the end) and then when it was finished, the update went off without a hitch. It took a few minutes to remember that I'd already downloaded most of my games, but it seems to be in its original working order!
I'm not sure why they don't mention this at all in their troubleshooting article...