First Body Glide is the best solution. Been through this a lot. Body Glide is the answer. Get it at running stores if your LBS doesn't have it.

Second, enough with the base layer fixation. Many of us live in climates where it is IMPOSSIBLE to wear a base layer in the summer. That is not a universal solution. What works in Portland, does not work in Houston or New Orleans or Miami. And there are many days in the OP's NYC that aren't much better. Shorts (not bibs) and a sleeveless jersey are as much clothing as can be tolerated. If the jersey still chafes the nips, back to Body Glide.