I have tried a few clipboard managers and two of the best (Ditto and Ethervane Echo) paste on an open F# Interactive window when I am trying to paste on the Editor. Others, like ClipMate (not free) paste on the Editor window. Is there a way to force pasting into the Editor window?
(I am aware that one can use Ctrl+Shift+V to cycle through recent clipboard items)
Try Clip Angel clipboard manager. I use it for coding in C#. It pastes with no problem to C# interactive. And if you will meet some place where nothing can paste, Clip Angel has "Emulate keyboard input" feature to break the defence =).