There is no mention about the lady cop in the changelog, so i'll assume u cannot.
The grind its something thats been noticed before, even by the dev itself and as far as i now hes working on lessen it, u even have a proof of that in this changelog: • The new event can award 5 [LOVE] points for 1-2 characters every week, I will add more of these events the coming updates to reduce the grind a little.
Hopefully the grind will be getting lower and lower, so maybe try the game in a few months if its unbearable for u right now, with some luck by then the game "harvesting" will be alot smoother. Cheers!