I just think (and in not a expert) that,
The extra weight and size of the triple 14" over the twin 15" is the reason for the increased breadth of the hull. The ship does not need to be any longer than it already is.
I think the weight of triples will be much bigger than twins, (as in just Gun Weights 14' 86.110kgx3=258.33mt v 15' 101,605kgx2= 203mt) so 20% more without thinking about anything else. This will force massive redesigns.(taking time, slowing speed if wider etc.)
I think that the turrets will take the time to build not just the guns so going for triple 14 (when the 14s started in twins) will not save time v building more 15inch twins.
Britain had two ships of the class about 75% complete when this ship is ordered/laid down. Making a modification to an existing design to take the triple turrets is not a huge change.
Why not just build another one with twin 15inch ? (apart from not making a nice new drawing, and I do like your ship
)
JSB