First of all I wanna say I have the maximum respect for CC and I appreciate the service and the safety they provide on board.

I am not much of a whiner about this kind of things, but I was recently on a redeye transcon LAX-JFK seating in F and I noticed fairly loud chatter coming from the front galley pretty much for the entire duration of the flight.
I don't think it bothered too many people but I think it was a bit rude, considering it was a 5 hrs redeye and most people just wanted to sleep (I believe most did nevertheless).

I wonder, how do you politely approach CC about their own excessive chatter without looking like a spoiled brat?

I think overall the service was great and the F product AA offers between LAX-SFO-JFK is the best way to fly transcon.