Step 1: trade Connor Brown, replace him with Bracco/Petan/anyone
Step 2: trade Nikita Zaitsev - he's having a good playoffs and a team may actually take him for nothing (include a pick or package him with Brown if necessary)
Step 3: trade one of Johnsson/Kapanen+ for a defenseman (Pesce)
Hyman 2.25 - Tavares 11 - Marner 10
Johnsson 2.5 - Matthews 11.6 - Nylander 7
Moore 0.775 - Kadri 4.5 - Bracco 0.85
Marleau 6.25 - Gauthier 0.675 - Petan 0.775
Marchment 0.77
Rielly 5 - Pesce 4
Muzzin 4 - Dermott 0.86
Rosen 0.75 - Welinski/Wideman 0.85
Holl 0.675
Andersen 5
Sparks 0.75
Kessel 1.2
=82.03
If this is how the Leafs handle their tight cap issues then kudos to you and the Leafs as this seems like a real win in a situation that could be a little bit difficult to navigate. I do have some doubts about a couple of your points, but I'm nothing more than a hockey fan so maybe I'm wrong, but here are my thoughts.
Trade Brown - No issue, given his contract and playing style I'd think that is an easy one. I wonder about replacing his style of play with Bracco or Petan, but this is very realistic.
Zaitsev - I don't think this will be as easy a move as you seem to. His cap hit is high but palatable, his term is not good and his recent regular season play might make him a more difficult trade than some think. I don't think he's untradeable, but I think it will take retention or more of a + than Brown).
I don't see Kap or Johnsson netting Pesce. If the Canes were considering 2 time 60+ point Nylander for Pesce I can't see them willing to take 40+ point Kap or Johnsson instead. Both Kap and Johnsson are good players and could get a decent player via trade, but Pesce might be too big of a target.
Marner at $10 might be a little light. I see him asking for MM money and don't think he'll settle for $10 (crazy to think $10million is settleing).
Not a huge deal, but you've listed 22 players in your cap breakdown, its common to have 23 roster spots - not necessary but its the norm.
Anyway, point still stands - not a criticism but Leafs front office will be working every angle this summer to maximize the little bit of cap space they have.