Round vs Around

I came across the whole 'round versus around' debate while editing a manuscript for an American indie author. Being British, I use them both, and consider them words with different meanings, appropriate at different times, but my American friend felt that 'around' was predominantly used in all cases, unless referring to something actually circular. Hence my research began.
A divide has clearly occurred (yet again) between the American and British usage of this word. The Brits do indeed see them as two different words, with different meanings, and interchangeable, whereas the average American doesn't; they rely heavily on around, only using round when talking about an actual circle.
So let's look at a few facts:
The word round works virtually anywhere around would work, but the opposite is not the case. There are several definitions round doesn’t share with around. 
For example: 
The edge of a circle is not around.Someone would not play an around of golfYou wouldn't have big around eyes.'Around and around the Mulburry bush' doesn't work the same. And just today I told my son to move his legs round under the table - meaning to turn them from the side, where he had them, under the table. If I said, move your legs around, he would have waggled them at me!