I sometimes use Control-Command-M to move documents to specific (or new) groups.
That 3-key “shortcut” shown on the Menu → Data → Move to … which is mentioned elsewhere in this thread.
That being said, I mostly–since it works so well–use the Ctrl-C to move a file short-cut which is presented in the “See Also and Classify” Inspector, available via Ctrl-S or Menu → Tools → Inspectors → See Also and Classify.