I think that Toronto would match anything up to the first+third threshold

If Edmonton signs Puljujarvi, he'd have to clear waivers to be loaned to the KHL or Liiga. There is zero chance of that happening. If the intention is to send him to Europe for a year or two, that would have to be negotiated with Karpat (or Jokerit if he's going the KHL route) and Edmonton would have the option to retain his rights but not sign him this summer. I don't think this is a good idea at all: you're risking him either not coming back to the NHL once he finds his game, or he fully becomes a bust. If on the odd chance he does find his form, AND you have him signed and playing in the NHL, the odds are much higher of him staying in the NHL. If not, he's a bust and you've lost him, but you've done your due diligence.

Overpaid Dzingel by at least $1.5M, and I'd prefer to give Marody another year in the AHL despite how close he was to making the roster this season. His contribution to the Bakersfield roster, as well as a chance to further his skating outside of the NHL, is likely to serve Edmonton better in the long run. If he's the piece that can get Edmonton's prospects to a Calder Cup Final, I'd keep him there and let him, Benson, and Yamamoto shred the minors. Thus, your savings on Dzingel and Cave > Marody could probably allow you to resign Khaira and add a depth defender.

Toronto matches begrudgingly (unless Marner takes a bridge), and I really don't think New Jersey entertains that trade for a second.

I don't think the difference of 2 selections is worth it for Vancouver to take on that much more cap and term despite how useless Sutter was last season. Edmonton's either taking back more salary in that deal, or some form of Eriksson-Lucic swap occurs.