The real reason why none of the ORIGINAL cheek pieces seem to fit properly onto the No4 butt is because the drawings and thus the fit all relate to fitting them to the weapon for which they were originally designed. The P'14 sniper! A close fit but not exact or even good in many cases.
At Warminster we have the original rifles used to test the fitting of the cheek piece and the paperwork that suggests that it was popular with the snipers and staff and is there any reason why this new cheek piece cannot be fitted to the 'new' No4 sniper rifles that are coming on-stream. The rest, as they say, is history. So for you real originality freaks, your Enfield converted sniopers shouldn't have cheek rests!