One small correction. If both Toronto and Carolina lose the play-in and Carolina wins 1st overall, the Toronto pick can't be better than 12th. There are only 4 teams with a better regular season winning percentage than Toronto, and Carolina is one of those teams. So if Carolina wins 1st overall, that pushes Toronto back 1 spot.
Here are the things we would need to happen to get each pick:
12th overall
Carolina, Toronto, Pittsburgh, Edmonton and the Islanders all lose in the play-in
Carolina wins 1st overall
13th overall
Carolina and Toronto lose
Two of Pittsburgh, Edmonton and the Islanders lose
Carolina wins 1st overall
14th overall
Carolina, Toronto and Pittsburgh lose
15th overall
Carolina and Toronto lose and Pittsburgh wins
16th +
Carolina or Toronto win
For the 12th and 13th picks, we need too many things to happen. I doubt Pittsburgh is going to lose, so we are probably looking at either the 15th pick, or more likely, a pick somewhere between 16 and 31. If we beat Carolina and Toronto wins, both of our picks could end up being 20+, depending on how far each team goes. Worst case scenario (for our picks) would be losing to Toronto in the ECF. Assuming they handle the last 4 picks as usual, that would give us the 28th or 29th pick and Toronto's 30th or 31st pick.
It's pretty crazy. On one end, we could get 1st overall and 16th overall, and on the other, we could get 29th overall and 31st overall.