It should be quite obvious to anyone halfway intelligent and reasonable that the window is closed for this group.
Both Palmieri and Nelson need to be traded this summer for the best available offers. Both players have M-NTCs so the market may not return as much as we'd like (depending on who they'd approve trades to), but something is better than nothing. Neither player has a role on the next contending Islanders team.
I'd also see what offers were out there for Sorokin, Barzal, Horvat, Pulock, and Pelech, assuming they'd waive. I don't think you need to rush trades for these players this summer (like with Palmieri and Nelson) if there aren't good enough offers, but these players probably don't have a role on the next contending Islanders team and should be traded within the next 1-2 years at absolute maximum.
Dobson and Romanov are probably young enough that they could have a role on the next Islanders contender so I'd hang on to them if they're willing to re-sign and stick around through a few rough upcoming years. Otherwise trade them over the next few years before they reach UFA.
The other junk on the main roster has no value so they're stuck here until contracts expire.
Time to go full scrotched-Earth.