Keep That Pie Hole SHUT
From experience, most police officers are not in the "brownie Points for being Honest" Business.
They are there to enforce a set of rules, not understand or interperet your specific "situation". Don't offer any information you are not directly asked for, and as soon as you have to offer something incriminating, ask for your lawyer, and keep your mouth shut.
This is from, personal experience, several police officers I have come to know on Metro over the years, from both sides of the bars.
The nice guy routine might truely be honest, but I guarantee, they will turn on you in a second if they think anything is even a little hinky.