If Brisebois is smart, he'll move out Jeannot, Perbix, and Sheary. It gives the team around 17.5 million and enough room to do what they need to do to improve, provided Stamkos works with them on his deal. If not, he walks and Tampa.still has plenty of space to add quality from ufa this summer.
I think Jeannot is gone. He can fetch a 3rd or 4th from a team looking to add a bottom six talent.
Perbix is someone they shouldn't move - he has a low enough contract for next year that he is an asset for the team
Sheary doesn't carry any value, maybe they get a 7th or future considerations.
The problem is their lack of prospect depth. They can't retool by trading out a few bottom six guys and plugging prospects in. They need to get value in return for these guys leaving that fills a terribly bare cupboard.
If I were them, I'd be trading Cirelli for a an NHL ready prospect and pick in this draft. Clears $6M out, and brings in cost controlled talent. If Stamkos is to be resigned, that will by $5.5M+, and Cirelli is simply the most moveable piece that doesn't impact their true core.
If the cap goes up $4.5M, the lightning have roughly $12.5M. RFAs and low level UFA resigning + Stammer at $6M puts them at 800K of cap. And their team loses Dumba/Duclair/Fleury/DeHaan. That new team may not even make the playoffs let alone give them a run.
If they move our Jeannot/Sheary thats $4.6 of relief, but only gives them roughly $3M of additional spend for two spots. Maybe they can bring in an aging vet or two, but Tampa needs to get better at 5v5 and a couple aging guys doesnt do it.
My suggestion, trade Cirelli/Jeannot/Sheary, and use $10M to bring in 3-4 decent younger players on some term. Get a good prospect back from Cirelli, and retool for a year so you have one last window to run with the core.