I'd suggest, rather than the "right-click to copy under mouse" having a more intuitive ctrl-x, ctrl-c, ctrl-v interface. This would allow you to copy a whole selection and place them all, for even more rapid placement.
I like the way the menu appears over the main screen, but it does make editing at the top quite difficult. Perhaps a key to switch it from top to bottom placement? I think that would be better than making clicks go through the menu (the semi-transparency is good, but I don't like being able to interact under the menu). Hmm, that is actually something I should consider rather than having my GUI completely separate from the game window.
I'm actually creating a similar editor as the core part of my game, though sadly mine has reasonably different requirements so I can't just reuse yours. I'm sure we can cross-fertilise ideas though :)
Bug (though you probably know about it): When you pick up a new object from the menu, if there is already a placed object under it, it is dragged too.