I am agnostic regarding Sullivan. I am less charitable about poorly considered replacements and just throwing shit to the wall to see what sticks.
f*** Babcock. If I have to explain that, this discussion is useless.
Why don't we take the first coach on your list, Jim Montgomery. I believe in redemption, second and even third chances, but let's think this through. Imagine Ron Hextall approaching the Fenway Sports Group, who just spent $900 million for this franchise, and saying, hey, we need to replace Mike Sulllivan, and I've found your guy. Ignore Jim's DUI in 2018, prior to coaching the Stars. That was a one off. Let's forget that, a year after that, Dallas fired him barely into his second season because of continued concern about his public drinking. And he is certainly more promising than his 4th place Central division finish in his only full year as NHL HC. This is our guy. He will bring us Stanley Cups. Yes, he isn't even two years out of rehab, but this is our guy. Pressure won't faze this dude.
I don't think whoever presents this idea to management/ownership will get a second chance in the room.