To be honest, I'm not convinced by the 5.1" gun with a 62lb shell.
The 4.5" shell weighed 55lb (4.7" 50lb) due to a much better ballistic shape. Applying this to 4.7" calibre would have been the OTL 62lb shell.
So stick with the 4.7", and design the new shell. With separate shell it should be fine to handle.
The 4.5" mount was intended for AA use, use that as your new GP mounting with the heavy 4.7", and you should be golden
You can probably also modify the existing 4.7" to take the new shell, increasing the surface capability of the old destroyers
Using one common mount for all new destroyers and AA armament on heavier ships would allow them to be mass produced with cost savings, and make logistics simpler (just the 4" and 4.7" as opposed to 4", 4.5" and two types of 4.7")
The 4.5" shell weighed 55lb (4.7" 50lb) due to a much better ballistic shape. Applying this to 4.7" calibre would have been the OTL 62lb shell.
So stick with the 4.7", and design the new shell. With separate shell it should be fine to handle.
The 4.5" mount was intended for AA use, use that as your new GP mounting with the heavy 4.7", and you should be golden
You can probably also modify the existing 4.7" to take the new shell, increasing the surface capability of the old destroyers
Using one common mount for all new destroyers and AA armament on heavier ships would allow them to be mass produced with cost savings, and make logistics simpler (just the 4" and 4.7" as opposed to 4", 4.5" and two types of 4.7")