If Rivers wants to leave so bad, let him go. Get something back for it, even if they are young pieces for the rebuilding process, or some great young draft picks.
Offer Pierce the chance to COACH & PLAY, as has been done before. Place him and Bass as backup for the younger starters (Green, Sullinger, Rondo, Bradley.) He has plenty of experiencing working with Rondo. He is a home town favorite. He has the respect of his teammates and most players in the league. You retain a veteran who can teach the younger players how it's done.
Boston saves the money from the last year of his contract and puts it toward his coach salary. Boston saves all the remaining cost of rivers contract, and pays Pierce half what his last year would have cost.
Both moves give Boston a lot more money to work with in the rebuilding process. As for KG, leave it up to him. He will miss Rivers, but would love to play his final days alongside Pierce and finish in green.