Ray Allen is probably the best conditioned of the Big Three. I don't worry about him, it was a lot to ask of anybody to shut down Kobe on defense while starring offensively as well. The same thing happened to Pierce, guarding LeBron completely affected his offense.
Great suggestion on Lee. I would love to have David Lee, he's a great player who does all the little things too. He'll be too expensive though, we can't fit him in our cap. If Darko, who completely sucks, just signed for 5M per year, Lee will be a near max contract player to get. Rudy Gay just got 80Mill from Memphis too. Lee is a long shot for the Celtics, there is a tiny chance he'll take a dramatic pay cut to play for a championship.
The problem is for contracts under 3 years, you can only offer a new contract 120% higher than the previous contract. Only with 3+ year contracts can a team use Larry Bird rights to resign players to max contracts. It is very unlikely any player will sign with Boston to win a championship and sign a below value contract for 3+ years, and also very unlikely that they would sign a contract under 3 years and stay with Boston after that.
To have some real numbers to look at, here are the Celtics salaries
HoopsHype - NBA Salaries - Boston Celtics
With 5 players under contract without Pierce, Allen, or Rasheed, the C's are already at 42 million. The NBA salary cap for next year is 56 million. This puts the Celtics out of the running for most non-incumbent players who won't play for mid level money.
It doesn't matter if Pierce and Allen resign for huge home town discounts. It doesn't matter if 46 million are coming off the books if Pierce, Allen, and Rasheed all leave. It isn't like the NFL with the hard cap, where if you count 20 million are off the books, you have that amount to play with for other free agents. The Celtics have room for basically one mid-level guy, then can only fill the roster with cheap players, and also resign their own guys.
Ainge understands this, which is why he's going after the only thing he can do, which is keep the current ship going.