I have an early P6B (1971) that used to suffer from Vapourisation very badly, despite fitting an electric pump (Facet) but... it would occur after only 2-3 miles driv9ign. and took longer than 5-mins resting to cure; often over 1 hour to allow all of the engine bay to cool.. Finallyraced to lack of coolant circulating through the Carburettor tower. Check that water is flowing from the tower back to the radiator, via the thin (2cm.) hose to just below the rad. cap.
Your problem does not seem to be Vapourisation, and is not like mine which was most definitely vapourisation. but only ever happened on English summer days, never in winter.
Are you getting a full flow of fuel in normal conditions? Could it be muck in he fuel tank partially blocking the fuel line? Does changing to reserve make any difference? In take is lower in the tank and more susceptible to blocking.
I remember a partly blocked fuel filter causing similar problems to yours.