First, I changed the default action when you select a tile on the map and then click on the map from copying it to moving the selected tile.
Also, rather than having a right click context menu for rotating tiles, I create a transparent toolbar with 4 icons that overlay the tile. There's a right and left rotate icons as well as cut and copy icons. This allows you to cut/copy tiles to the clipboard and then click on the map to paste that tile (repeatably if you want to c/p more then one).
I'm working on allowing you to select more than one tile and c/p them.