Or, on the low end of the scale, something with a Rotax 912, 912S or 914 engine. That means you can use mogas, which is available everywhere. (Assuming the rest of the fuel system is mogas-rated, and no legal restrictions forbid its use.)
There are aircraft with these engines that do very impressive speeds for such low horsepowers - the MCR4 for instance I believe cruises at 135 knots.
That's still about 45 hours flying in still air for 6000 miles but the total fuel consumption will only be (rough calculation) 750 liters or so.
So that solves the fuel availability issue. Furthermore, the 912 and 912S have a very good reliability record. I don't know how well it compares to turboprops, but they're easily on par with Lycosauri, and better than Thielert.
And of course, with the rather low cruise speed also comes a low landing speed, increasing survivability in a crash landing in hostile terrain.
Guy named Thomas Scherer flew his Rotax 912-powered homebuilt Europa across the Atlantic. Twice. Once via the "traditional" Greenland-Iceland route, and once via the Azores to Newfoundland direct - 13 hours non-stop I believe. That hostile enough for you? (His website
:: This Site is Under Construction :: seems to be down though but if you Google for N81EU you might find stuff in Googles cache.)
And only slightly outside the OP specs, Tecnam now does a Rotax-powered twin. A MEP rating on that one would probably be easier and cheaper to get than a SET rating.