I can't vouch for the accuracy of the Cast Off turret as I don't do kits. I can verify that the drawing in David Fletchers book is accurate certainly as far as a 1/35scale represention would be, I have studied a full size MkIII turret and it is asymetrical, as is the MkIV turret in the same way,but being cast its shape is different, I think the reference to layout which I assume is a reference to Chris's turret roof layout article refers to the general layout of ventilators and and periscopes etc.
The reason that the turrets are asymetrical is to keep the internal volume of the turret to a minimum, that is the minimum interior space enclosed by armour, to save weight. Many turrets are like this, all the Churchills have asymetric turrets as is the Centurion, even turrets which appear at first glance to be symetrical are not so, the most subtle examples as diverse as T34s and the US built M3Lee and M3 Grant.
The MkIII turret is similar to the early MkIV in a number of ways, but as design work continued the detail of the MKIV and MkV changed markedly, but the basic shape remained the same.
The level of accuracy of the drawings on page 64 of Mr Churchill's Tank can be gauged by what has been included and what is left off. Beneath the bustle, shown in "ghost" are the 9 air vents, these are covered by a steel channel to prevent bullet splash entering the turret. These air vents were evident on a good number of early MkIV turrets and were also a feature of the MkI and II turrets. Again in "ghost" the hatch gutter tubes are also shown, these are a feature of all Churchills.
What is left off is the rear applique panels that are shown in drawing TD5912,shown on the same page. Though it has never been mentioned in any text that I am aware of, these panels were not fitted as they would have obstructed the vison/pistol posts in the rear of the turret.