Well I have been digging around and finding out a little more about the Romany language. Theories on the origin/s of the Rom/Roma/Romany folk are many and varied but it seems they have strong historical connections to India. The Romany language has elements of several Indian dialects. Not many Romany words have been incorporated into English but interestingly the East Enders of London have a number of them.
Example: "bloke" (meaning a man, also commonly used here in Oz) is from the Romany loke, which in turn is the Hindi word for man.

Anyhoo - back to the grass/nark connection: from what i've seen it is pretty certain that the "nark" or informer is derived from the Romany nak or naak for nose. The nark would "sniff out" information - hence "copper's nark" being self-explanatory. The modern "narc" has it's origin in "narcotic" and should not be confused with the much older "nark". Similarity is coincidental I guess.

But Hev's question remains: WHY turn "nark" into "grass in the park"? Clumsy indeed. I wish I knew!