boreas,
I find "Ambergris" both hard to say as well as difficule to type. I typically use "San Pedro Town" as opposed to "Ambergris Caye".
  Pronunciation of any word is very regional. The dictionary may give a pronunciation of ambergris that is commonplace in the fragrance industry, for example, but the folks on the island may use a completely different form of speach.
  My policy is "when in doubt, say it with a smile". That's universal. I always pick up a few words of the local lingo and hack my way through the pronunciation as best I can. The locals seem to prefer me, a complete foreigner, bumbling through their language and grinning like an idiot, as opposed to my other options, which are limited to trying to find somebody who speaks my language or using the few words in their language that I'm comfortable with.
  With all that said, I say amber-gris without any real stress to either syllable. Everybody understands me. Nobody whose opinion I value looks down on me if this is incorrect. But I'm more confident with saying San Pedro Town.
    Dan