Q: contextual menu a "move to" option.

I apologize for answering without really answering, but just in case this is of use to you...

There is a relatively unknown keyboard shortcut for moving files.  Select the file, press command-c for copy, then click onto the destination folder and press option-command-v to move it there.

charlie

Freebies by Electron Zen

Use it as an example and create your own Automator service.

Mac 101: Automator

That's great, thanks!  It isn't on the contextual menu, but it is on the Finder menu.