Polly Vacher did well indeed but her flights were much more of a massive logistics exercise than flying, or navigation. Same is true of all long trips like that.
So what can one do to make it less complicated?
The OP has given away very little
However there isn't a 6000nm trip on which you will find avgas all along - unless you fly in circles around Bembridge
So, a turboprop is the only way. (Thielerts are finished for now, and anyway the engine would probably not last 6000nm).
There must be an operating cost issue. If the OP did not care about money he would have chartered a 737.
A PC12 or a TBM700 has a DOC of some £500/hour. The only cheaper options are a Meridian or a Jetprop but neither of those are OK for dirt strips - if indeed dirt strip capability is required. A Caravan is maybe another option but it won't get above any real weather.