To me, the big question with Davis is the length of the deal rather than the amount per year. If he is willing to do 2 years at $4 million per, I would take it, since he does provide a lot of things to this team as a championship contender. However, when you start going beyond 2 years, the per year average shoots down considerably. I think I would hessitate to even give him $3 million per year for 3+ years. I just see the C's as a very different team at that point, that will really need as much cap flexibility as possible, so having a backup big man like Davis on the books for too much money at that point could be dangerous.
Honestly though, I really think Davis and the C's will end up agreeing on a 2 year deal. It makes sense for the team, because it does not kill them long term, but also allows them to take advantage of Davis' abilities as a role player for the "window". And for Davis, I really don't think he will be getting the offers that he thinks he is worth this summer, given the other options out there, and the overall financial situation in the league (and so many teams saving space for next year). If he is as confident as I think he is, he will be happy to get paid decently for 2 years, and then try to hit the open market again, with a more developed game, maybe another ring or two, and a lot more teams with open checkbooks.