With a flat cap I don't see a way forward with that strategy. Cuylle may be the only ELC forward ready to take a shift next season. He alone isn't bringing a culture change. A new coach alone isn't bringing a culture change.
For the sake of this thought exercise let's say Gallant gets canned and the Rangers bring in a relatively green, though analytically savvy coach with a good understanding of basic strategy. That's a unicorn in today's landscape. As you've mentioned before, 25 of the 32 NHL coaches are basically the same dude. You have the Cooper's, the Keefe's, the Montgomery's, the Brind'Amours, and the Trotz's doing their thing and being successful at it that at least bring something different to the table than the other same, tired, 25 voices that get on and off the carousels every 3 or 4 years.
Who do you bring in to succeed Gallant to get the most out of a core of players that's essentially going to get swept two years in a row?
I've got nothing.