One the groups I am playing with went through something similar. Our solution has been overlaying Fate most recognizable mechanical elements over 5e inspiration mechanics. So the DM can compel the characters based on their ideals, bonds and flaws, rewarding them with inspiration, and the characters can spend inspiration to "bend" or add elements to a scene as if they were creating an aspect. Or you can get advantage on a roll as per normal inspiration rules.

No player at the table is forced to use the system, since it's entirely possible to just use 5e mechanics. But it definitely adds an element of fun for those comfortable with player contributing to the narratives not directly through the resolution of their character's action.

As a corollary, we raised the maximum amount of inspiration one can "hoard", to 3 +1 per tier of play (o 4 at 6th, 5 at 11th, etc).