I believe it could be done for about £40K but not much less than that (unless you are Colin Hales with a tent and a KR2!).
Avgas is rare at remote airports and needs to be carefully planned, but it is do-able. At least Lycomings are well understood and spares are available around the world.
Getting 2000NM+ out of any capable 4 seater should be possible by replacing rear seats with ferry tanks. If you look on the Earthrounders web site you'll see quite a selection of types including many homebuilts - RVs, Glasairs, Ezes etc.
Most important is a sound aircraft that you have confidence in and good instrument skills for the bad weather that your unlikely to avoid at some point. Weather and bad fuel planning are much bigger killers than mechanical failures!