I'm surprised a lot of your board don't like this. I posted this on the Avs board, but here's my perspective, and in my view it's amazing asset management.
Hagel - 2 1sts and an equivalent of 2x 3rd-5th for 3 playoffs of Hagel at 1.5 mil. He's still a RFA at the end. Assuming Hagel is a ~65-70 point player at the end of the contract, you guys should recuperate 70-80% of the cost and the picks will fit into their timeline of their rebuild assuming you trade him.
Similar with Jeannot, I actually think this down year made him more attractive to Tampa. Sign him either to a 2-3 year deal for under $3.5 mil, or sign him to a 4-5 year deal under $5 mil. Assuming he's at least a 50+ point player (should be, as he's the obvious Killorn replacement), Jeannot is a unicorn and you could probably recuperate again, at least 70-80% of the assets you gave up if you trade him near the end of his deal.