MCH Overheat should activate automatically

[Shurrikhan]

As for the finisher, you can even turn Scatter gun into a superior version during Overheat, let's say "Super shotgun".
Straight line AoE, makes Scattergun button relevant in single target situations.

Dragonfire. It's an actual shotgun thing and it'd be very, well, heated. Give it a nice short-and-chunky DoT. Longer-range narrow conal AoE still preferable, though, imo. (We already see tons of different cone-angles conals across the game, from 10 degrees to 180 [well, I suppose that's exactly where it stops being a conal].)

The Overheat starter being the first GCD of the Overheat phase, it should give 4 stacks of Overheat.

As long as the starter also gets the reduced GCD, this would be preferable, yeah. The threshold between what feels "significant" and what feels "spammy" can be as little as a 5th GCD.