Simple solution. Wayne Industries could need a lawyer. Or we could do a Bruce Wayne: Murderer/Fugitive thing to begin. The Court of Owls could team up with Owlsley. I don't think it necessarily means they need a big threat, just something personal. Honestly, I prefer an emotional Daredevil, a guy who cares about the people he fights and helps when possible.

In an official map of the DCU, Gotham is either west of Jersey or directly on top of it somehow while coexisting.

Perhaps Bruce could actually be in the NYC on business before seeing something he can't turn away from. After all, it's often stated that Wayne is the real mask. Or it could be about Karen Page and the men could compete for her affection/protect her from kidnapping, as often happened in classic Daredevil. Or perhaps Wayne could seek DD out as a sort of screening for potential in an Outsiders mission. Investigation is usually the part of a plot that's cut out of movies, like where they look and what their sources are. There's plenty of room for character development.

Plus, in a talkier game, comparative muscle mass shouldn't be too much of an issue.

Alternatively, I could just read a lot about the show until I really get the gist of it.