Thing is, you cal lthose things 4.5 cannons, but it's a 5.25 turret. Which is it?
I call those things 4.5in cannons because they're 4.5in cannons.
The turret resembles the 5.25in turret because I like how it looks but I didn't want to use the 5.25in guns, so in this AU Recherche develops their own turret using existing 4.5in guns at the same time (and using similar design practices and aesthetics) as the British develop the 5.25in turret, hence the similarity.
If these are 4.5 guns, you might want to change the look of the turret a bit.
Why?
The 5.25 turrets were really rather cramped, which interfered with the firing rate, although this might be alleviated somewhat by using a smaller gun with lighter ammunition. If anything, you could try and make them somewhat
larger
Looking pictures of the 5.25 at Navweapons over, if anything it convinces me that the 5.25 on the parts sheet needs a do-over.