I'm clearly in the minority based on the responses thus far, but I say trade him:
1. It's clear the two sides are not going to come to terms on a number that works for both parties. You can spin that to mean the Red Sox are cheap, or that Mookie is being unreasonable, or somewhere in between. But the situation seems to be that he wants to play somewhere else at a higher number.
2. By all accounts, Mike Trout is undeniably the most talented player in the MLB. Yet how many times have the Angels missed the playoffs in the last few years?
All this is to say that baseball is different than basketball. An MVP-talent is by no means a guarantee that you'll have a successful team. With or without Mookie, the Red Sox already have enough bats to succeed. You win in the postseason with clutch pitching and timely hitting. You typically get to the postseason with a few pitchers that can single-handedly win you a game every 5 days.
Even in the Red Sox recent World Series year, Mookie didn't provide the clutch hitting for the Red Sox during the playoffs. So even if he's one of baseball's best all-around talents, the Sox can win without him.
3. There are also just as many examples of these huge contracts immediately becoming huge mistakes. Granted every player is different. But for every Mike Trout there is a Ryan Howard. No matter what people say about Mookie, it IS a risk to throw $400 million at a guy whose batting average dipped 40 points after his MVP year. Which year is the real outlier? If I have to ask that question, I'm not going to overspend to keep a guy that doesn't really want to be here and just wants the most money.