I guess it depends on the size of the egg you want and how productive of a layer they are. I have Red Star pullets now, and my original chickens were Red Stars. I know two other people who raise them, too, and they get great results. I haven't and the two other people haven't kept them longer than 2 1/2 years (until they molt), as you said.
But, all chickens molt around 2+ years old and stop laying during that time. All chickens will continue to lay eggs after they have regrown their new feathers, but they're not as productive as before.
So, I guess if you're looking for a chicken that lays daily, without stopping for several months to molt, and that will continue to lay daily for over 2 1/2 years, I don't think you'll find one. All chickens have that resting period of not laying any eggs during their "first" big molt, and I even gave up after 2 months of waiting for one hen to start laying again.
As far as one that continues to lay pretty well after molting, someone else will have to answer that.