SS
Looks like you are going to wind your neck in. It is only a public transport flight if the pax are fare paying pax. If Mr Wilkinson ( type rated pilot)was hiring the ac off Mr Dunn again it is not a public transport flight. If the pax were paying a proportion of the flight ( not including the transit flight) then again it is not a public transport flight, providing the flight was not advertised, unless advertised within a flying club.
Would suggest before you stick head above the trench you should check your facts, saves neck winding at a later date. However I do not know what if any money was changing hands so I may have to wind mine in !!!!!!!