Your observation about the lack of CSA sea power would certainly not be overlooked by Confederate leaders as this was the reason they would have nearly lost the war. The development of the Confederate navy would have been task number one beginning in 1864. I seriously doubt the Democratic leaders in the north would have gone back to war to save Cuba in 1866.
Building a Navy capable of challenging the Royal Navy would have been quite a project, in all likelihood well beyond the capabilities of the CSA.
Anywho, I thought the South seceded because of the oppressive federal taxes. Do you have any idea how much building a major navy cost at the time, or now for that matter? It would also require the development of a truly massive industrial infrastructure, something the South was ideologically opposed to, and which could not have come into existence without large protective tariffs, something specifically prohibited by the CSA Constitution.
Essentially, the CSA could be a low-tax limited government backwater or (theoretically but unlikely given its low population) a hemisphere-conquering industrial and military behemoth.
It could not be both.