Details to follow, but preliminary findings: I haven't gone the Barry Marshall (guy who drank the H. pylori culture to prove that it caused ulcers) route, because I have a day job, but I've combined the use of coconut water and Tylenol, and I have never gotten such satisfactory results from Tylenol alone (or ibuprofen alone, or Midol alone). My period started this afternoon, and I'm still experiencing some dull cramping, but it's very very mild, and usually my worst cramping is right after my period starts.
So...will continue to publish my findings (and will try to be more scientific about it next month), but for now I'd say unless you're allergic to coconuts or something like that it's definitely worth a try; probably can't hurt much even if it doesn't help.
More information on what it is and how to get it here. I drank two of those 11-ounce tetra packs each on Tuesday and Wednesday, and one today, which was when my period started in earnest. That company I linked to seems to ship overseas as well, and it also seems to be the cheapest place to order online, at least that I've seen.