In Help > Support Assistant > Install Extras > Scripts you will find a script “Move with Keyboard”. Install that script, and it will appear in Scripts > Data as “Move”. Because that script now appears in the menu bar as a command, you can give “Move” a keyboard shortcut in System Preferences. (Instructions here.)
This script uses the global “Groups and Tags” display to show you all the groups in open databases – the scripts intent is to provide the broadest scope possible for cleaning up the global inbox, for example.
If you want merely to access the smaller “favorites” list which is accessed via “Move” in the contextual menu, then you would need to use a utility like BetterTouchTool, which is capable of assigning shortcuts or trackpad gestures to contextual menu commands in apps.
Otherwise, at this time, there is no method like the one you suggested.
It works alright. I really wish that there was a way to say that I am focusing on processing my inbox. That could open up the possibility for assigning keystrokes to move commands and tags like the old iPhoto keyword window. I’m not getting faster at moving things into DevonThink. I realize that, in time, I won’t be pulling so much in at once but I plan to process enough that I will be at it for months even if I could speed things up.