Corn , by itself is as good for feathers as a candy bar is for a toddler.. don't believe everything you read. A calorie is a calorie is a calorie.
No, it not true that most birds don't lay until 30 weeks. It is true that genetics is always at play and they don't read our books about when we think they should do what. Most my early spring hatched Easter Eggers are laying by 17-24 weeks, never later. Birds hatched later and maturing in fall will lay later because daylight is diminishing.
Lay hormone is light related.. It takes at least 14 hours of light I think for 1 ovum to be releases into the reproductive track. Birds that lay later, will also lay larger egg right from the start in accordance with their body size. And they're hatched with all of the eggs they ever will lay already on board.
Now, for that whole corn thing.. Most our feeds are already made with corn as the main ingredient.. It has added mineral, vitamins, and important amino acids.. that scratch and plain corn by itself do not... making it a balanced ration. Corn by itself is about 7% protein, Adding corn to a balanced diet diminishes protein and other nutrients in most cases.. it should be used as a treat for enrichment at NO more than 10% total daily intake.
Corn does NOT keep birds warm.. it is ONE source of energy. The birds keep themselves warm via thermogenesis and their feathers for insulation.
Also feathers are made of 90% protein and their amino acids.. Corn again is JUNK.. by itself. Wan't better feathers increase amino acids and protein.
I recommend NOT diminishing your nutrients with corn or "layer" feed at this point.. and instead using a "grower", flock raiser, all flock, etc.. with oyster shell on the side.. until all your birds actively come into lay. I personally never switch and my birds molt softer now.
Birds that lay that late.. quickly find themselves not spreading their genetics here.
All details I attempt to share are meant in a friendly and informative manner. Sorry if it comes out harsher than that.