There are two "clipboards" (see http://standards.freedesktop.org/clipboards-spec/clipboards-latest.txt )
If you want to use the keyboard an option is to just use the real clipboard instead of the goofy middle click / current selection easter egg. Then you can use ctrl+C, ctrl+V. (Or Shift+Insert)
I don't see a key shortcut for pasting the selection in the GTK+ source code, for what it's worth, so if you do want to avoid the Ctrl+C I don't see a way to do so.
Come to think of it, perhaps it could never work, because when you left-click into the entry to paste into it, or tab navigate into it, it's going to be auto-selected, which will blow away whatever you had selected before. Middle click is the only way to paste without changing the selection first.