Well, one possible resolution to this issue would be to add something fundamentally new to boss fights - a "stance" bar.

The more damage a boss takes, the more that stance bar depletes, and when the bar is empty, the boss gets winded, stops all mechanics for a few seconds, and receives a vuln up debuff. Now, everyone can go to town on the boss, unleashing their big d deeps.
That would free classes to have their own timers on their damage cooldowns, so every player can chose whether to burst early to bring the boss in the winded state quicker, or wait for the vuln debuff. Would bring in a different way of synergy.

Now, this is not the most original idea (other games do that already), but it would be an option.