Bringing up Gardiner is a good comparable, not because of the contract he signed but because of the contract he was offered. The Habs offered him a 3 year, $5.25 million deal at the start of free agency, but he was holding out to try to get more. I think you might be able to get Schultz at a contract like that, possibly even getting him to sign the same contract he signed 2 years ago. But less than that? No way.
I think getting Schultz for another 3 year, $5.5 million AAV deal would be a good contract that I'd definitely re-sign him for. I'm just concerned that he'll be shooting for a Faulk type of contract, and based on his past history, I don't think it's reasonable to expect him to be generous towards the team.