I agree with everything except Cotter. People can say I'm hard on him but he was visibly not an NHL player most of the time, he scored some goals on nice setups when he as shooting above 20%, but when that evened out he was worse than useless, he was detrimental to the lines he was on.
If he is spending any significant time with Eichel and Marchessault our chances of repeating are dropping.
We need a power forward to play with Eichel and Marchessault, someone who can go in on the forecheck and stand in front of the net for that line.
Howden and Amadio filled those roles for the Stephenson and Karlsson lines, Dorofeyev isn't small but I don't know if that's his game. Cotter can't play that game at all.
Goalies, yes let someone pay for Hill but not us. The list you put is a good one, Talbot, Varlamov, Raanta. I wonder if Reimer would be looked at, as well.
I think they should look for a bigger guy, 6'2" or even taller, that seems to be the type Burke can bring the best out of, and Thompson is big too so the defense wouldn't need to adjust as much if both goalies are playing similar games staying deeper in their net.