Ok, here's what I did...
Using AppCleaner, I double checked to make sure everything having to do with itch was deleted, including hidden files.
I rebooted, then downloaded a fresh copy of the itch install app. The package contents:
(executable) Install itch.app
(folder) Contents
(folder) _CodeSignature
(file) CodeResources
(file) Info.plist
(folder) MacOS
(executable) itch-setup
(folder) Resources
(resource) itch.icns
I double clicked on "Install itch.app" and a popup window entitled "Itch Setup" appeared and started DL'ing and installing. The itch app's window appeared, asking me to login. I tried using my email then my user name, and got the same error message both times:
Post https://api.itch.io/login: x509: certificate signed by unknown authority
Like I said, the only thing I've done since accessing the itch app last is update Java.