Have you tried right-clicking the menu and going into Properties? It gives you the option to change the keyboard shortcut.
Yes. My desired shortcut <Alt>Space is accepted and remains the "preference" after rebooting, but does nothing. As I mentioned in the first post, doing this on the 32-bit LMDE activated my desired shortcut properly, but for some reason does not work on the 64-bit version.
I might add that going back to the default <Ctl>Super_L and rebooting DOES get mintMenu to pop up. So why not just use the default? I work on several different OSes -- 3-4 linux ones, Mac OS X, and 2 versions of Windows -- so keeping many different sets of shortcuts straight is an issue. The <Atl>Space keys are in the same place on Mint and Mac (Cmd-Space on the Mac, but the same physical location). So using this shortcut really does make sense to me. And it ought to work -- so I'd like to figure out why it doesn't.
If anyone who's running LMDE 64-bit could test this on his/her system, it would be greatly appreciated. It would tell me whether this is a specific issue with my system, or a general bug with mintMenu on 64-bit LMDE.