That is a very good general summary.
I’d merely make a few points:
The PIC of my 15 seat B350ER can be remunerated handsomely for flying me around in it, but it’s not a passenger transport operation. See: exclusion (d) from the definition of ‘passenger transport operation’. (But I of course immediately concede that no other pax are permitted.)
Secondly, I’m not aware of any judicial authority for the proposition that the sharing of any costs among POB a flight necessarily constitutes ‘reward’ of the PIC within the meaning of CASR. I’m aware of CASA’s opinion to that effect. Have you seen any authority cited for that opinion?
In any event, it merely points up one of the many ridiculous distinctions in the rules that have no causal safety risk justification. According to CASA it’s ‘acceptably safe’ for a PPL to be the PIC of a 15 seat aircraft with 14 pax if the PIC meets the entire direct costs of the flight and receives nothing from anyone for anything connected with the flight, because there is no ‘reward’, but it’s not ‘acceptably safe’ if one of the POB throws the PIC $1 to cover $1 of the direct costs because that $1 constitutes ‘reward’. As I’ve said: That $1 has profound regulatory consequences - according to CASA - even though the $1 has zero safety consequences.