Keyboard Only Control When Hotkeys, Hinting, and Tabbing Fail
I've settled on an ultimate method of final last resort when mousing is simply not an option. Karabiner (recently renamed from KeyRemap4MacBook) offers a "Mouse Keys Mode" which allows vim-style hjkl control of the mouse pointer and uio for left-middle-right click. There are a few options for the hotkeys that will activate this mode. My current preference is Cmd + S + D.

https://pqrs.org/osx/karabiner/

As much as possible this method should be avoided but if you, like me, often don't have a mouse or trackpad readily available then it can be useful.