Apparently this is a known issue for a while. I'm on 27.1 right now on windows and the following code allows me to use the menu key as hyper:

(setq w32-pass-apps-to-system nil)
(setq w32-apps-modifier 'hyper)

However neither of the lwindows or rwindows versions work.

(setq w32-pass-rwindows-to-system nil)
(setq w32-rwindows-modifier 'hyper)

I'm not sure what key to use for Hyper in general. Ideally it would be something that wouldn't interfere too much with windows or ubuntu desktop shortcut keys, and unfortunately a lot of those use the Win/Super key. Caps_Lock for that would be nice. Is there a way around this problem?