My thinking on moving Konerko or Lee .... Would you trade either of those guys straight up for JD Drew? I would, even with his history on injuries. He would fit in perfectly with the Sox. LH hitting Rf'er is exactly what we need. So, if we can sign Drew or someone similar, trade Lee or Kong and plug in with Gload at 1B or Everett and/or Borchard in LF, I think the Sox would be more balanced and more competetive.
Then, on top of that, you can add the players you receive in the trade to the equation.