Why do I keep getting "Error: Unable to proceed with the installation?" while trying 2 update Flash?

The Flash installer downloads fine, and then after I click on it and it starts the install, it asks for my password and proceeds for a while. I even get a little bit of an "Install Progress Bar" happeneing, and then I get the above error message.

I've tried uninstalling the old Flash, turning off all Safari extensions, restarting, examining the "package contents" as recommended on your site, etc. None of it works. Now I have no Flash at all, and need to get on with my work.

I'm on a MacBook Pro Retina (G1) running OS X 10.9.1.

Please help. Thanks!