Focus floating system windows with keyboard

The windows I'm talking about are the system administrator password request popups, the wireless network web sign-in popup, and other system request dialogs, such as "Application was downloaded from the Internet" confirmations. Often when these popups appear for me there is no focus on the input/buttons. I need to remove my hands from the keyboard and mouse over to them.

These popups do not appear in the application switcher, and seem to be immune to these focus-grabbing keyboard shortcuts:

• Command ⌘+`
• Command ⌘+Tab
• Control ⌃+F1 through Control ⌃+F12

I have seen one solution that involved turning on OS X's VoiceOver utility with ⌃+Option ⌥+F2,F2. I'd prefer not to have this turned on, since in my regular work hours I use ⌃+⌥+F-keys in my IDE.

I would post pictures, but my reputation isn't high enough yet.

UPDATE: I do, in fact, already have the option set in System Preferences to allow keyboard navigation in all control windows.

If you enable full keyboard access in System Preferences, you can press tab to select the buttons.

I don't know how to focus the windows though. They can't be selected with ⌃F4 or ^F6. I was going to suggest Witch, but it doesn't show them either.

This is a bit of a hack, but you could assign a shortcut to a script like this:

tell application "System Events"
    repeat with p in {"SecurityAgent", "CoreServicesUIAgent", "loginwindow"}
        if exists process p then
            tell process p
                if windows is not {} then
                    set frontmost to true
                    exit repeat
                end if
            end tell
        end if
    end repeat
end tell

Password dialogs are shown by SecurityAgent, Gatekeeper and quarantine dialogs by CoreServicesUIAgent, and the force quit window by loginwindow.