I think you've got to make Double T an offer which is respectable. Don't lock him into nonsense but offer something fair to him so he can move away in another season if he desires. This was a weird off-season for these guys and he'd likely have other options in normal years.
He was great for the young guys and you can tell he gives a crap about the team. I love the guy and his work ethic. But it DOES come down to what he thinks he's worth. Again, like Love, he's a vet who makes you win more games if you are playing the right kind of basketball. He also is one guy you can rely to try and play some damn defense.