The path seems pretty clear. Perhaps not easy, but getting rid of all three of Jeannot, Perbix, and Sheary provides the needed space to actually make the team better. Stamkos is unlikely to go anywhere, and that's fine provided the cost is no more than 6 5-7 aav. There will still be enough room to then add both add a dman and a F that will help both areas. After that, yeah, a few bottom 6 spots will require some cheaper contracts in ufa, or a couple of Syracuse players will get more of a chance.
Without losing key pieces(which then of course creates more holes in the lineup that need addressing), Tampa will have one area where they will need cheaper ufa contracts or Crunch players to step in and contribute. The 3rd and/or 4th line is more ideal in this regard imo than having the problem be in the top 6 or top.4 D moving forward. They'll have Paul, Eyssimont, and Glendening back, and if Motte wants to stay for cheap, great. If not then no doubt JBB will find 1-2 ufas in ghe 900k-1 million range, and 1 or 2 Crunch players can be given their chance(Chaffee again, Goncalves is ready, etc).
Whether JBB is willing to make those moves and accept the returns(and what may have to be paid to move Sheary) is another story, but barring losing much more integral pieces like Cirelli, Serg or Cernak, or letting Stamkos walk, this is the most clear path to having the space needed to improve the roster for next season.